I don't know who invented that fucking word 'starchitect'. In fact a journalist invented it, I think. I am not a 'star-chitect', I am an ar-chitect..." Just 10 minutes into the interview, Frank Owen Gehry, the world's most feted building designer, is already a bit irate. A short, owlish man, who looks younger than his 80 years, he speaks quietly when left to his own devices, and meanders, never quite finishing one train of thought before it segues into the next. When he is tackling something more contentious, though, he relaxes and becomes animated. His head rises and so does his voice. He even smiles. This is a man who likes a scrap.

So I lob the first hand grenade by using the s-word , and ask him if it is true that the so-called 'starchitects' – such as himself, Jean Nouvel and Zaha Hadid – have raised the profile of their profession and raised the game of architects everywhere. Or have they merely created personality cults? "There are people who design buildings that are not technically and financially good, and there are those who do," he replies. "Two categories, simple."

Despite his modesty being offended by my use of the "star" word, Gehry, the most talked-about architect since Frank Lloyd Wright, is quick to ensure there is no uncertainty about which of the two categories he falls into. With no prompting, the statistics come thick and fast.

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"My building in Bilbao cost $300 a square foot with a budget of $100m. I finished it on time and on budget and it doesn't leak. After 11 years it's still there. Last year it earned the city of Bilbao €320m – that's the custom generated by the museum for the city through the visitors it attracted. Walt Disney Hall was built for $215m and the budget was $207m and it doesn't leak and people love it and it works, and people identify Los Angeles with the building the way people identify Bilbao with the other building." Phew.

Milan's rather trad Triennale design museum doesn't appear to leak either, but otherwise couldn't be more different from Gehry's titanium-clad, avant-garde creations. Nonetheless, it is currently hosting a major display of the models, illustrations and photos of all his important designs since 1997. This was the year his gleaming Guggenheim gallery arrived, apparently from outer space, to park itself on the grey banks of the Nervion River in Bilbao, lighting up that rather down-at-heel Spanish city.

A similar mix of hi-tech and whimsy reappeared in Berlin's DZ Bank building (2000), LA's Walt Disney Concert Hall (2003), the Ray and Maria Stata Computer Center at MIT (2004), and the as-yet-unbuilt addition to Washington DC's Corcoran Gallery, all of which are featured in the show.

The Milan exhibition is an upbeat way for Gehry to end what has been both professionally and personally a rough 12 months, overshadowed by cancelled projects, job losses and family tragedy. It is also a timely reminder of the remarkable work he has already achieved. Despite his spectacular career, with a Pritzker Prize (architecture's equivalent of a Nobel) under his belt and professorships at Yale, Columbia and Harvard, Gehry's triumphs have never been enough to overcome his need to prove himself.

He was born in Toronto, Canada but his family moved to Los Angeles in 1947. Gehry, poor, Jewish and new in town, was the triple outsider – snubbed by LA's artistic elite. He changed his name from Goldberg, supposedly on the advice of first wife Anita Snyder, in order to avoid perceived anti-Semitism in his profession. "Each time I suffer like I'm starting over again in life," he once declared of the design process. "There's a lot of healthy insecurity that fuels this stuff."

It is a peculiarly American brand of insecurity, however, which required Gehry to seek years of help from psychoanalyst Milton Wexler, before allowing the same therapist to go public about his client's hang-ups in the Sidney Pollack documentary on Gehry and his work.

That's not to say that Gehry is without a sense of humour. This is the architect who did the voice-over for his appearance in The Simpsons, parodying himself as he tossed scrunched up bits of paper onto the floor in search of inspiration for new buildings. There is also an endearingly prosaic quality to Gehry's bombast, and despite his stratospheric position in the world of architecture, the emphasis he places on sticking to a budget shows that he is aware of one of the biggest gripes faced by his profession – that its members get carried away, with little consideration for their customers' bank balances.

But once again, Gehry has turned that charge on its head with his much-discussed "organisation of the artist" working philosophy, which places the architect in control of the design throughout a building's construction. This not only enables the original artistic vision to remain intact, but also eliminates the malign influence of politicians and business people on the construction process. In Gehry's view, these are the real villains behind inflated budgets.

Matters of control and artistic compromise have been on his mind this year, in the build-up to his next, eagerly-awaited work, the Guggenheim Gallery in Abu Dhabi, slated to open in 2010.

The vaguely pyramidal structure, surrounded on three sides by the waters of the Persian Gulf, will at 450,000 sq ft, dwarf the other Guggenheim galleries. Gehry has already gone on the record with his concerns that rigid Islamic cultural mores might seriously limit the range of art that the gallery is able to display. However, his fears have been allayed.

"This was something that I was really concerned about. But they've just done a show of Picassos from the Louvre (presented in another Abu Dhabi gallery in the run-up to the Guggenheim's opening) which even contained some nudes and it went out with no problems; there was no editing or interference. They have curators from all the over the world now, so it's going to be a very interesting collection." Though it has been no bed of roses in the Emirates: "I was at a meeting and there was one curator there expressing his hatred of Israel to me, so you can see it's not going to be that easy."

The Abu Dhabi museum is touted to be one of his most beautiful creations yet. A criticism that has dogged Gehry, however, is that his museums are more interesting than the art they contain. It certainly seemed true of the Bilbao Guggenheim – but it hardly seems Gehry's fault that the art it displayed was so underwhelming. A few years ago I was lucky enough to be invited to a gala dinner in this, Gehry's most celebrated building, and at night, with its soaring atriums lit in different colours, the building' interior was a work of art in its own right: cavernous but strangely intimate; part space ship and part Walt Disney fairy castle. Aside from some jolly Jeff Koons creations, there seemed little to drag my gaze away from the endlessly fascinating architecture.

Other critics accuse Gehry of borrowing too heavily from other art forms – another odd complaint, seeing as artists from Michelangelo to Picasso have studied and incorporated earlier achievements from other art forms in their own creations. Gehry swats away such moans, in practised fashion.

But other charges are a little harder to dismiss – or at least they rile him rather more. Shouldn't he make some more socially relevant buildings? Aren't his designs too extravagant? Times are tough, after all. This lights the touchpaper as effectively as the s-word. "We are architects ... We serve customers!" he barks. "I can't just decide myself what's being built. Someone decides what they want, then I work for them. Look, I went to city planning school at Harvard and I discovered that you never got to change a fucking thing or do anything. Urban planning is dead in the US."

So that's urban planning dealt with. Gehry doesn't really do discussion. But having uttered the final word on a subject, he sometimes seeks partially to make amends by offering discourse on a vaguely related theme. This time it is financial hardship.

"I think that people will have learn to live more modestly; I think they should learn to save their money. We've been through a generation of excess – everybody's got two or three cars, we've been flying all over the place, but now something else is happening and we've got to respond to it; although architects alone can't do it." Some of them might have to tighten their own purse strings, though. Gehry has had to lay off 100 people from his own firm, Gehry Partners, in the past year.

His candour is refreshing, however, in the way it allows him to criticise modish or politically correct assumptions. His views on "environmentally friendly" architecture are one example. "Green issues have been used as a marketing tool. Sometimes these green claims are completely meaningless." But there is still the quick chance to blow his own trumpet about a building he has just done in Switzerland: "It's all glass, but with the highest energy-efficiency rating."

One underlying theme in Gehry's world-view appears to be is that progress is inevitable. "If you try to stop progress you can't," he says. "Even though some people don't seem to want it." He's keen to talk about a friend of his who he says is "under siege by animal rights activists" on account of his work as a medical researcher. "They've attacked his mother's grave, her gravestone and burnt his house down. These kind of people want to live in the past."

Certainly, advances in technology, from metallurgy to computer software design, have allowed him to construct his masterpieces in stone, glass and titanium. But he also thinks technology could solve problems from population growth to environmental destruction. He just doesn't think that it is all the responsibility of an architect – even a very famous and influential one – to make sure it is employed to these ends.

Although the new show is set in Milan, conservative Italy has never been receptive to Gehry's avant-garde deconstructivism or 'decon' architecture, with proposals of his for Modena, Rome and Venice coming to nothing. "In Italy, the country of the baroque, there's no place for post-baroque Frank Gehry," one Italian design critic wrote this month.

"If I pay attention to what's happened in Italy and project what's going to happen in the future based on my experience so far, I would say that nothing's going to happen here," Gehry agrees. Anyway, he enjoys designing for more barren terrain, where there is a need for new visual stimulation. And whatever Italy's deficiencies, a lack of architectural eye-candy is not one of them.

Is that why he has not designed major things for London, a city already brimming with radical new buildings by Norman Foster and the like? This starts him off again. "Is Norman Foster radical? I don't think so. What does it mean to be radical? Some people have the ability to experiment and some don't. Anyway, most of the world doesn't want experimentation."

In this context I can't resist mentioning that architects' nemesis, the Prince of Wales. But it elicits a surprising response. "It's ok for Prince Charles to be who he is, and want what he wants – God bless him for coming out of the closet and saying what he thinks ... I mean some of things he likes, I like, and some of things he's come out against, well, I'm on his side," he says.

New York, where he lived for many years, is another city in which you might expect to see more of Gehry's singular style. His relatively orthodox Beekman Tower, a 76-storey residential skyscraper, is due to open next year in Manhattan. But it was with the sprawling and ambitious Atlantic Yards development in Brooklyn that he was to have made his mark on the city. Last December, however, in bid to cut costs, property developer Bruce Ratner fired Gehry from the project, scrapped six years' worth of design work in process, and replaced it with, in the words of New York Magazine, "a graceless knock-off by a journey-man stadium-builder".

Critics in the city painted a picture of a celebrity architect hung out to dry by a property magnate who had used the Gehry name to obtain tax breaks, to win out over rival bids and to secure the power to evict tenants. Asked about events, Gehry merely says the collapse was "down to a set of opposing interests that blocked the project".

He's also reticent about a more grievous loss, the death from cancer of his 54-year-old daughter, Leslie Gehry Brenner, herself an artist and designer, a month before the Atlantic Yards collapse. Fans of the great architect might also have been saddened by reports that he is thinking of calling it quits in the not-too-distant future. Is it true that he thinks he only has a couple of years of designing left in him? Gehry replies indirectly, saying his company is "in the hands of bright young things who are going to design lots of wonderful new buildings".

But we probably haven't seen the last of Gehry yet. A look around the Milan show reveals Gehry designs still in the pipeline, including the proposed Atlantis Sentosa Resort in Singapore, complete with 300-foot pearlescent glass sails. So there could still be plenty more to surprise, delight and shock, before he calls it a day. Plus, there is every chance the designs that are already finished will still be here, leak-free, for a long time to come.

The exhibition 'Frank O Gehry from 1997' runs until 10 January at the Triennale museum, Viale Alemagna 6, Milan, Italy; for details call 00 39 02 724341 or visit www.triennale.it

Gehry's greatest hits: A career in buildings

Dancing Building, Prague

Also known as 'Fred and Ginger' and the 'Drunk House', this waltzing building was designed by Gehry in collaboration with Vlado Milunic, and was completed in 1996. Its distinctive shape, which resembles two figures leaning towards each other, dancing, gave rise to its numerous nicknames. The river-front site was previously occupied by a 19th-century townhouse, which was destroyed in the 1945 bombing. The Dancing Building now houses offices and a restaurant.

Guggenheim Museum, Bilbao, Spain

One of Gehry's most famous buildings, the Guggenheim Museum in Bilbao is made up of curved, interconnected shapes cased in bright titanium, giving the shimmering appearance of fish scales. At its core is a large, light-filled atrium, which has views of Bilbao's estuary and the surrounding hills. Opened in 1997, it was deemed "the greatest building of our time" by architect Philip Johnson, and although it was designed to house substantial site-specific pieces, Gehry's architecture is often thought to eclipse the artworks it contains. Costing $100m, it paid for itself within just one year, and has been credited with kicking off a cultural and economic revival in the Basque country.

DZ Bank, Berlin

A rare example of Gehry's work fitting in with its surroundings – there are strict rules about what can be built in central Berlin, meaning an outlandish structure as in Bilbao wasn't an option. But the building, which houses office and residential space, still carries distinctive Gehry hallmarks: a grand atrium is topped by a curved glass structure resembling a whale's hump or a ship's hull, while the rear facade has a fluid, irregular structure which contrasts with the more conventional front, designed to match the urban planning of the Pariser Platz.

The Experience Music Project and Science Fiction Museum, Seattle

Paul Allen, Microsoft co-founder and collector of rock memorabilia, wanted a "swoopy building" to house his museums dedicated to popular music and sci-fi. Matching design to content, Gehry took inspiration for the sheet-metal construction from electric guitars: "We started collecting pictures of Stratocasters, bringing in guitar bodies, drawing on those shapes in developing our ideas," he recalls. The result – curvy and colourful, with a monorail running through it – does look both suitably sci-fi and 'swoopingly' musical.

Walt Disney Concert Hall, Los Angeles

Funded by the Disney family, this 2,265-seat concert hall offers another instance of nautical inspiration – its auditorium is designed to resemble a ship's hull. The exterior is visually arresting too, with sail-like curves made of shining stainless steel (some panels later had to be sanded to a dull matte, because their reflection of the sun's rays had seriously overheated nearby buildings). This 2003 construction isn't just about appearance though: it was carefully designed to provide exceptional acoustics, with a hardwood panelled interior, and is the home of the Los Angeles Philharmonic.

The Ray and Maria Stata Centre, Cambridge, Massachusetts

Gehry's 2004 building for the Massachusetts Institute of Technology has a random look, all strange angles and deceptive curves, as if the different sections are collapsing into each other. It's clad in a mish-mash of surface materials, colours and textures too – mirror-shiny metal, brick, bold coloured paint, brushed aluminium. Costing around $300m, it was funded by Bill Gates and Alexander Dreyfoos, who each have towers named after them. However, in 2007 the MIT sued Gehry's firm after persistent leaks and drainage problems.

Marqués de Riscal Vineyard Hotel, Elciego, Spain

Gehry's only hotel is another fluid building, which seems to stream colourful, curling titanium ribbons over its central construction of sandstone blocks. Gehry called the building, which was completed in 2006, "a marvellous creature, with hair flying everywhere". Part of one of the oldest wineries in the Rioja region, the hotel offers guests a dose of avant-garde design to accompany their wine tasting and spa treatments.

Guggenheim Abu Dhabi Museum, Saadiyat Island, United Arab Emirates

Continuing under construction despite the crisis, Gehry's second Guggenheim museum will be a huge 450,000-square foot structure. Block and cone-shaped galleries cluster around a central covered courtyard, connected by catwalks, while other galleries pile up on top, providing an innovative combination of vertical and horizontal exhibition spaces with unique curatorial possibilities. Gehry's design brief was to "push the boundaries of his own architectural practice and set the benchmark for museums," according to Sheikh Sultan bin Tahnoon al-Nahyan, of the Abu Dhabi Tourism Authority.

Holly Williams

What was the most memorable arts event of 2009? In the comments form below (or via email to arts@independent.co.uk) nominate your favourite - in film, music, theatre, comedy, dance or visual arts - with a brief explanation as to why it tops your list and we'll print a selection in The Independent Readers' Review of 2009.