Ten years ago she was the architect who couldn't get anything built. Now, from the Olympic Aquatics Centre to a new Serpentine gallery, from Beijing to Baku, Zaha Hadid's buildings are everywhere. But she divides opinion: she's a genius, say some, but to critics she has lost touch with her original ideals

Zaha Hadid: 'Her temper provokes fear, but she also inspires admiration… she is human – funny, frank, unafraid to show her emotions.' Photograph: Marco Grob

Zaha Hadid was flying to Frankfurt to give a talk, in which I was her interlocutor. Her plane taxied from its stand, developed a minor fault, and stopped. She refused to believe the reassurances that the delay would be brief, and demanded that she be put on another flight. Her wish was impossible – to return to the stand, to unload and reload her baggage in the hold, it couldn't be done – but Hadid insisted, vigorously. The cabin staff tried to calm her, warn her, admonish her, until a stewardess noticed that this was the same woman whose picture was in the current edition of the in-flight magazine, attached to a profile of the Pet Shop Boys, for whom she had designed a set. "Are you Zaha Hadid?" she asked. Then the impossible became possible, and the architect got to change planes.

There are hundreds of stories like this about Hadid and they tell the same story, which is also that of her life: the testing of boundaries, the determination to get her way, the fury, the indifference to practical constraints, the opposition of conventional society, here represented by the cabin crew. And then the ultimate victory aided by fame, a fame earned through personality and talent.

To say she divides opinion is to put it mildly. To some, including several fellow architects that I spoke to, she is a tyrant; her work is "unbelievably arrogant" and "oppressive; I don't believe she cares what it's like actually to be in one of her buildings". To others she's a genius, and a hero, the only ground common to all these views being a remark once made by her mentor, Rem Koolhaas, that she is "a planet in her own inimitable orbit". The truth is that she is all these things, and more. She tests everyone – her staff, her clients, the users of her buildings, and herself – and offers an unspoken deal. If you survive all this, I will make something fantastic, and you could be part of it, is roughly how it goes, and people's view of her will depend on which part of the deal they experience most.

Over the past decade or so she has gone from being the Architect Who Never Got Anything Built to someone who can't stop building. At the turn of the millennium she was still best known for winning at an early age the competition to design the Peak in Hong Kong, a leisure complex that was never realised, and for her martyrdom in Cardiff. Here, although she twice won the commission to design the city's opera house, local politicians did everything they could to ensure they got a mediocre project by another practice. Now her office boasts 400 staff and 950 projects in 44 countries. Their work includes colossal developments inChangsha, China, and in Bratislava, a large luxury villa in Moscow and a role advising on the airport that Boris Johnson would like to build in the Thames Estuary.

Zaha Hadid's Heydar Aliyev Museum in Baku. Photograph: Afp/AFP/Getty Images

Her first building was a fire station near the German-Swiss border, for the furniture company Vitra, a building that celebrated its 20th birthday this summer. This autumn two of her more important projects are opening, at opposite ends of the constructional scale. In Baku, Azerbaijan, there is the colossal Heydar Aliyev cultural centre, a billowing creation that promises to be the most complete realisation yet of the Hadid universe. The Serpentine Sackler is opening in Kensington Gardens, a conversion and extension of an 1805 gunpowder store that will be a sister gallery to the nearby Serpentine. The latter is to the Baku building as a waterdrop is to a whale, but significant because it is in the heart of London, a place that, although it has been her base for 40 years, has been slow to build her works. It is not however her first building in the capital. There is also the Evelyn Grace academy in Brixton, which won the Stirling prize in 2011; a little further from the centre her Olympic Aquatics Centre is reopening next year, adapted from its games mode to a swimming pool for public use.

The rapid expansion of her practice has several causes, including its own determination to lose its "unbuildable" tag. Most of all it is a consequence of the 00s boom in "iconic" buildings, when spectacular architecture was believed to work regenerative miracles for the cities and companies that bought it. She, equally extraordinary in her personality and architecture, is the perfect iconic architect. She is collectible, with her furniture designs commanding astounding prices. When money vanished in the west, oil-rich and Asian countries carried on. Her earlier buildings tend to be in European or American cities insecure about their urban dynamism – Wolfsburg, Leipzig, Strasburg, Cincinnati, theoutskirts of Basel. Now she's popular in China, Russia, Azerbaijan and Saudi Arabia.

Now aged 62, Hadid has won all the biggest awards in her business. She is a celebrity, a phenomenon, continuously feted, with connections with Brad Pitt and Barack Obama. She has also bought, for a reported £10m, the building that the Design Museum will vacate when it moves to new premises in 2015, whose purpose is to house her archive, and to "engage in a collective dialogue by exhibiting the research and innovation of global collaborations in art, architecture and design". A prototype of this institution can be seen in the design gallery she hasopened in Clerkenwell. On its ground floor there is her extravagantly curvilinear furniture; upstairs is kept an ever-expanding array of architectural models.

Her temper provokes fear, but she also inspires admiration. Where many leading architects seem robotic, she is human – funny, frank, unafraid to show her emotions, sometimes fond of talking a little dirty. Aaron Betsky, writer, museum director, and an old friend, says: "People wonder why anyone works for her, given that she can be a stern taskmaster, but she can also show incredible loyalty and support, and passion for what she does." She has worked hard since student days, sometimes succumbing to bouts of illness. She has never married or had children, although she has denied that she sacrificed family life to her work. "I'm sure I could have managed," she told Lynn Barber in the Observer in 2008.

Stories abound of her grandeur, such as dispatching an assistant from the Venice Architecture Biennale to her London flat, and returning with the shoes she wanted to wear for a particular party, but she can also be down-to-earth. Rather than occupy an exclusive room, she preferred for years to sit among the tables in the old school house that is her practice's office, throwing out instructions to staff. She has shown courage, not least in overcoming the real obstacles of being a woman and an Arab in a white, male business. She dresses spectacularly, never favouring the mannish jackets and boyish haircuts with which some women in her profession attempted to smuggle their gender past the invisible barriers. Her approach was to blow them down.

Julia Peyton-Jones, co-director of the Serpentine Gallery, has said that Hadid's life and her work constitute "an all-encompassing vision" and "a complete work of art", that she is "a pioneer", "well ahead of her time". In the Hadid-designed Roca showroom in west London, a curvaceous sci-fi quasi-shrine with the ostensible purpose of selling bathroom fittings, a visitors' book is rich in tributes. One reads: "One of the most beautiful experiences in the life. I am the future. Best best xxx love." Also: "a mesmerising trip to the future"; "I love Zaha Hadid. Very peaceful place"; and "I trust in Zaha Hadid. I was sure that this place should be amazing!"

From Peyton-Jones to the scribblers in the Roca book, there are common themes: Hadid is amazing, and she shows us the future. The same themes can be found in her own and her practice's descriptions of her work. Her senior partner, Patrik Schumacher, with whom she has worked for 25 years, has written that her designs are "manifestos of a new type of space" that pursue "the conquest of a previously unimaginable realm of constructive freedom".

The love is not, however, universal. The Beijing Cultural Heritage Protection Centre, for example, has stated that it is "shocked" that Hadid's Galaxy Soho development of shops and offices has been given an RIBA award. Where RIBA's president, Angela Brady, praised its "visionary new thinking about urban issues", the heritage group called it "a typical example of the destruction of Beijing's old town". She has been criticised for her Baku project, commissioned to glorify a regime notorious for its human rights abuses, and for its forced evictions of homeowners to make way for new development. Here at least she has the company of Lord Foster and Rem Koolhaas, who have designed comparable monuments for the oppressive rulers of Kazakhstan andChina.

In Baghdad, the city where she was born, she entered the competition to design a new parliament for Iraq, which was won by an emerging London practice, Assemblage. The former British minister Lord Howarth, a member of the competition jury, calls the latter's plans "the product of rigorous thought" and "becoming for an institution replacing a dictatorship", "rather than a grandiose and egotistic flourish". Hadid's entry has been called "convoluted", but her failure to win the competition did not stop her office continuing to talk to parliamentary officials, in the apparent hope that she will be awarded the project after all. If so, this would be a reversal of her treatment at Cardiff, and something with which she should have nothing to do.

Behind these stories questions recur: does her success, her associations with the mighty, her splendour, mean that she is losing touch with the complexities and contradictions that were once part of her work? Is she now in danger of favouring the spectacular to the exclusion of the dirty realities of cities, in which she used to profess an interest? If she has been dominating/generous, and grand/earthy, is the first half of each pairing now ascendant?

My own experiences of Zaha Hadid include writing in her support during the Cardiff battles, and following and reviewing her works. I have also been her client twice, or three times if you include a speculative proposal for the rebuilding of the burned-down Teatro Fenice in Venice, which I helped commission for a newspaper.

The first time was when I was editor of Blueprint magazine, and we collaborated with the constructional trade show Interbuild to realise a Zaha-designed pavilion in the National Exhibition Centre in Birmingham. It was to be paid for partly by Blueprint advertisers, whose products would be incorporated into the structure, and a tricky moment came when she presented her designs to them. Her explanations were obscure to this sceptical audience, and when she finished an awkward silence fell. The pavilion seemed doomed, but then a northern voice broke out – "I think it's bloody brilliant" – and its owner, the head of the high-quality toilet cubicle company Thrislington, led a round of applause. The other advertisers had to join in, and then write the necessary cheques.

The pavilion was built, not without difficulty or busted budgets, as it required a kind of steel-frame construction more suitable for small bridges than a week-long trade show. But Interbuild, Blueprint and the advertisers got their publicity, for achieving what was in 1995 Zaha's first structure in Britain. And it was a memorable thing, putting into the shade a classical hut that Prince Charles's architectural institute erected next door.

The last time was when the Architecture Foundation, of which I was director, ran a competition to design a new building to house its activities. Zaha Hadid won, and another meeting gathered in her office, in the same room where Patrick Wilson, the Thrislington man, had won the day. This time it held the many consultants who would help get the building built, who were there to learn about and be enthused by the project on which we were embarking. Hadid wandered in and out, while her project architect attempted an explanation of the designs, occasionally telling him from the doorway that he was doing it wrong.

It was not an auspicious start, and after three years, many sleepless nights and some hair loss, the project was abandoned. We experienced the same impatience with practical constraints that she had shown on the Frankfurt flight – the cafe would not be easily heatable in the winter, the window-cleaning bill equalled the salary of a member of staff of this small organisation, the project architect turned up at a meeting called to cut costs with a redesigned staircase that would increase them. At the same time she and her office showed dedication, working long hours to address problems, producing an entirely new design when necessary, and dealing with frustrations not of their making. As clients, it should be said, we at the Architecture Foundation had our own imperfections.

We were not alone among her clients in facing practical challenges – the Aquatics Centre for example uses prodigious quantities of steel, which dented London 2012's pride in using the material economically on their stadium, and coped awkwardly with the need to have temporary additions to house the seating required during Games time. But nor are such challenges unique or new among celebrated architects. Early houses by Richard Rogers were cold, damp, and/or nightmarish to build. The functional shortcomings of Le Corbusier's and Frank Lloyd Wright's works are legendary. Andrea Palladio's church of Il Redentore in Venice, consecrated in 1592, was seven times over budget and had poor acoustics. As choral music was one of its functions, the latter was a serious fault, but it is still seen as a masterpiece.

Patrik Schumacher has even addressed this question of practicality as part of the practice's philosophy. "Functional optimality," he wrote, "is… renounced in favour of the experimental advancement of social practices of potentially higher functionality." This seems to say that, if you have to choose between firing someone and having dirty windows, it is worth it, because at some point in the future her architecture will lead to a better world. It is almost religious: sacrifices now for reward in the hereafter.

The Maxxi National Museum of 21st Century Arts in Rome. Photograph: REX/View Pictures

Such sacrifices are infuriating to other architects who try responsibly to avoid them, but sometimes they are indeed worth it. If we had got her Architecture Foundation building built it would have been a permanent addition to London's stock of extraordinary places, and we would all have felt good about it. For cultural institutions there can often be a trade-off, in that the spectacle and celebrity of a Hadid building brings benefits of fundraising and publicity that can help pay for costs in cash and neuralgesics.

Pippo Ciorra is the senior curator of architecture at Maxxi, the museum of contemporary art that Zaha designed in Rome. He acknowledges that it was "very expensive", but says that Hadid was the right choice for the project when she won the competition in 1998. It was "the outcome of a season of optimism" in Italy in the late 1990s, when the government of Romano Prodi promoted cultural innovation. "Then everything went wrong," says Ciorra, but at the time it was "necessary to have hope". The building finally opened in 2010, after a tortuous gestation and in a very different Italy.

The building is in essence a series of concrete tubes, writhing and overlapping, which connect an external courtyard to the internal exhibition galleries in what aspires to be a continuous flow of space. It is dynamic, in what was a sleepy district, with long curving interiors accelerated by longitudinal fins in the ceilings. It is modern baroque in an old-baroque city. "It is more and more successful," says Ciorra. "People like to come and enjoy this public space, to take advantage of it."

It is, he adds, "really incredibly well built… Immense attention was poured on it. There were dozens of models made, and it didn't lose anything in the transition from the design to the finished building." He also opposes the most common criticism of Maxxi, which is that it is a poor place for displaying exhibits, that the construction dominates the content. "It works well" for the architecture exhibitions that Ciorra mounts, and he likes the fact that it creates no boundaries between art and architecture shows. It is "a little more challenging for art curators, but they are getting better." The secret is to be bold, "not to pay too much respect to the place… in the beginning they were too shy."

Maxxi fulfils many of the promises of the first part of Hadid's career. It is powerful, distinctive, spectacular and displays her ability, evident in the Peak, of conceiving complex spaces in three dimensions. More importantly, it contains ideas about cities and public life, also evident in the Cardiff project. According to Aaron Betsky, her work is about "the gathering together and bundling of the energy inherent in a site and situation", and "the intensities that come from condensing things then opening up. At best it is intensely democratic, about removing barriers."

Through her architecture she has sought to create new and heightened relationships between the inner and outer lives of her buildings, between the contents of an opera house or an art gallery, and the streets outside. At Cardiff the audience would themselves have become performers, as they moved through a sequence of external spaces and internal foyers. In Rome she made a three-dimensional passeggiata that fuses an old city and new art. Critics of Hadid have always accused her of making extraordinary shapes for the sake of it, to which she responded by saying that they were means to the end of creating new urban experiences, as at Maxxi. According to Schumacher, the purpose is to "reflect emerging social demands".

With some of the more recent work, however, this defence is harder to make. The CMA CGM tower in Marseille, and the Roca showroom in London look very much like shape-making for its own sake, with multiple curves that have little purpose but to create an updated version of a 1960s vision of what the future was going to look like. In the glimpses so far possible of the Serpentine Sackler, her undulating, tent-like addition joins the old gunpowder store clumsily. Some hidden intelligence might be revealed when it is opened, but for now its curves seem lumpy and overwrought, earthbound rather than floating.

It would be surprising if Ilham Aliyev, ruler of Azerbaijan, has much interest in Schumacher's "emerging social demands", or in reflecting them in the Heydar Aliyev centre, which is named after his father and immediate predecessor as president. From a distance of a few thousand miles this building looks extraordinary, with almost every surface, inside and out, being both white and curving, offering an experience of total immersion in Zaha-ness. But it doesn't look like a work of the democratic urban energy of which Betsky speaks. Rather, it seems an exercise in isolated magnificence not so different from the colossal cultural palaces long beloved of Soviet and similar regimes – it is just that the giant Asiatic-classical columns that they would once have used have been traded for futurist swooshes.

Nor does her Galaxy Soho building in Beijing, which has upset the preservationists, fulfil her practice's promise that its projects "work in synchronicity with their surroundings". Huge, bulbous and uniform, it looms menacingly over neighbouring hutongs, the streets and alleys bordered by courtyard houses that are characteristic of old Beijing. This menace is actual as well as metaphorical, as similar streets were obliterated to make way for Galaxy Soho. "During the land acquisition process," says the Beijing Cultural Heritage Protection Centre, "the legal rights of the original hutong residents were also grossly disregarded." Walking in and around it, the experience is not of flow but of disconnection, of a space station descended on the city.

The architect Sean Griffiths is one of several of Hadid's fellow professionals who question her work, but he is more outspoken than most. "It's basically an empty vessel," he says, "that sucks in whatever ideology might be in proximity to it. In Moscow in 1923 it might have been interesting, but in the age of hyperventilating global capitalism, that's what gets sucked in." Another architect calls her current designs "commodified images of progress". Looking at the projects in Baku and Beijing, it's hard to disagree.

An artist's impression of the Serpentine Sackler gallery

Even a supporter, Pippo Ciorra of Maxxi, doubts that she can still be seen as ahead of her time. Her style, he says, "is a glorious prolongation of the 20th century", whereas now younger architects "work for the future in a different way". They profess interest in the environment, for example, about which "Zaha doesn't give a shit". He also questions what he calls the "industrial" methods of design her practice now uses – its huge output means that the close personal attention she gave Maxxi is no longer possible on every project. The production line of city centres and cultural monuments tends to create projects that look like parodies of the Zaha Hadid style, hard to distinguish from the increasingly large number of imitations by lesser firms. It is a particular feature of her approach, of the idea she embodies of architect-as-artist, that it relies heavily on the intensity of her individual creativity, which works less well when it is diluted.

Partly, this is a phenomenon that often comes when pioneering architects achieve success. It is probably humanly impossible to continue to invest the effort and emotional energy that goes into the early work. It could be argued that it is better to employ talent and experience on dozens of buildings, than on a few agonisingly crafted masterpieces, even if this disappoints fans from the days before the star in question was so famous. Norman Foster has made this trade-off as, to a lesser extent, has Frank Gehry.

I'd also say that there is still some X-factor, some oomph, that sets almost any Hadid project apart from the copyists. I am fully expecting her Aquatics Centre, for example, to be one of the greatest places in London in which to swim, even if its new-look exterior is a bit ponderous.

But it is hard to escape the feeling that she has become a prisoner of her grandeur. She and her work now seem to inhabit a bubble of celebrity, with a decreasing connection to the rest of the world. The bubble is sustained by often uncritical media: when the BBC made an Imagineprogramme about her, they managed not to air any of the controversies raised by Baku, Beijing and Baghdad, but presented her purely as a great creative talent.

The Serpentine gallery meanwhile is not a neophyte among Hadid's admirers. She has been a long serving trustee of the gallery, and designed the first of its annual series of temporary pavilions, in 2000. It says that since then "it had always been the intention… to commission a permanent structure for the gallery by Zaha. This presented an unrivalled opportunity to realise a ZHA landmark building in central London." She was appointed for the project without a design competition which, although it is unusual for organisations such as the Serpentine, it was entitled to do.

Entitled, but not wise – there are many architects more obviously suited to a small-scale addition to an historic building, but its awe and desire for a "landmark" seems to have dazzled an organisation usually sure-footed in its appointment of architects. By failing to look outside its loop of admiration, and by playing her out of position, it has done neither itself nor her any favours.

And, visiting the showroom and archive in Clerkenwell, which will eventually require a museum building to house it, I am struck by the disappearance of a sense of scale. Scale is something that connects an object to something outside itself; without it what is left is the Zaha look, the Zaha brand, that can be digitally expanded or reduced to suit the size of a project.

Hadid remains ahead of her time, and responsive to emerging social demands, in the sense that the world is becoming a series of concentrations of wealth and power, which express themselves through lavish, singular trophies. To this extent there is a reality to the work. But it is different from the ideals she used to express, or of her achievements at their best. There has always been conflict, or tension, between her artistic ego and her public spirit, which is what made her interesting, but it's getting hard to see the latter.

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