In a climate where the richest collectors - Charles Saatchi, Roman Abramovich - are as celebrated as the artists they buy, we tend to forget that in the history of arts patronage, entrepreneurs-turned-connoisseurs are a young development. The world's greatest museums - the Louvre, Hermitage, Prado - began as lavish civilisation-is-power statements by monarchs and emperors; private individuals did not emerge as significant museum patrons before the 19th century. Until a generation ago, those wanting to leave their mark in bricks and mortar usually did so in a room of their own - albeit a very grand one - in a state museum: the Duveen Galleries at Tate Britain, the Abby Aldrich Rockefeller Gallery at New York's Museum of Modern Art, the National Gallery's Sainsbury Wing. But in the past 15 years, that has changed: worldwide, collectors seek immortality in glass and steel, through a museum of their own, designed by an architect of their choosing.

These are not latter-day Henry Tates or Pavel Tretyakovs. Although they gave their names to museums, Tate and Moscow's Tretyakov were democratic visionaries who paid for buildings and donated core collections to kick-start evolving national, state-run institutions. Museum builders of the 1990s and 2000s, by contrast, are products of late capitalism, dedicated to more personal projects, with an individualistic flavour. They represent the legacy of Thatcher-Reagan mantras of choice, private philanthropy, me-generation celebrity.

Many of the new establishments are extravagantly specialist - Ronald Lauder's 2001 Neue Galerie in Manhattan, dedicated to German and Austrian art; Wal-Mart heiress Alice Walton's Crystal Bridges Museum of American Art, planned for Arkansas in 2010. And in recently capitalist nations, the symbolism of the private museum is heavy. Dasha Zhukova's museum of contemporary art, the Garage, launched in Moscow last month, trumpets the power of the new Russian billionaires. Guy and Miriam Ullens' contemporary art museum in Beijing, opened earlier this year, showcases the social and aesthetic transformation of a nation.

Together, these and scores more bring diversity and flatten old geographical hierarchies. In Istanbul, collector Sakip Sabanci's museum, founded in 2002, is the first ever to show western modernism - currently, Salvador Dali - in Turkey. Thanks to Dominique de Menil, the greatest collection of paintings by Cy Twombly, who lives in Italy, is on permanent show in Houston, Texas, in a gallery designed in 1995 by Renzo Piano. In 1996 the late collector and dealer Heinz Berggruen launched his Museum Berggruen in Berlin, giving Germany its only Picasso collection. This week, Charles Saatchi's new gallery opened in London with a show of recently acquired Chinese work [see review on page 6 ].

Is all for the best in the best of all possible worlds? Certainly, more private museums mean more art on display for more people to see. Today's collectors are reluctant to bequeath to established museums, where space shortages mean works may go straight into storerooms and stay there. By contrast, a dedicated museum maintains the integrity of a collection, keeping together outstanding groups of works, assembled with personal flair, in buildings designed to enhance them. Renzo Piano's light, limpid 1997 construction for Ernst Beyeler's cherry-picked modernist paintings in Basel is the shining European example. For contemporary work, private collectors have particular advantages: free of state bureaucracy, they can respond quickly to the fast pace, and show work in ways that are too radical for traditional museums - in the confiscated-goods warehouse of a former drug enforcement agency in Miami, for example, that since 1996 has housed the Rubell Family Collection, ranging from sensationalist Chinese photography by Zhang Huan to Jeff Koons' vacuum cleaners.

What's not to like? Only that, whether they are stylishly successful or tediously tacky, today's rush of private museums is destabilising the art landscape. That they challenge the economics of taste may waft fresh air into art-history's ivory tower, but the speed with which new money shapes scholarly endeavour is daunting - witness the recent splash of monographs and retrospectives of Gustav Klimt, reckoned a minor Austrian symbolist until Lauder paid a record $135m in 2006 to install "Adele Bloch Bauer I" as "our Mona Lisa" in his Neue Galerie. Private museums speed up, too, 21st-century crises of shrinking art resources and growing demand. Will Asher B Durand's iconic American painting "Kindred Spirits", for example, bought for $35m by Alice Walton from under the noses of the Metropolitan Museum and the National Gallery, who had banded together to try to keep it in ­a public gallery, speak to more people in Bentonville, Arkansas, or in New York and Washington? If you strengthen holdings in the regions, you inevitably dilute centres of excellence. But to tell art's histories, public museums need a concentration of important work; diminishing that is to the detriment of scholars and serious art lovers everywhere.

And if the new museums are not up to scratch? There is no polite way to say this: many private collections are far inferior to those in public institutions. They collapse standards and offer a vainglorious travesty of a cultural experience to a paying public. We all have our bêtes noires; one of mine is François Pinault's disappointing art-as-fashion-emporium at Venice's Palazzo Grassi, launched in 2006 (another Pinault museum is planned for Venice in 2009).

Cautious national galleries stringently buy and accept as gifts only "museum quality" works. Private collectors, answerable to no one, buying on whim, not necessarily knowledgeable, often don't. Berggruen and Beyeler - each a dealer who was, as Berggruen wrote, "his own best client" - and the de Menils are exceptional. In the long run, though, it doesn't matter. Collectors have fun doing what they like and time will separate the best from the rest and ensure their survival. Meanwhile, we can all enjoy the new Darwinian museum jungle.

Jackie Wullschlager is the FT's chief visual arts critic. Her new biography, 'Chagall: Love and Exile', is published this month

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Visionary collectors: Fresh air into art history's ivory tower

However big a collector's ego, no private museum succeeds unless it melds with its environment - architecturally, culturally, socially. In different ways, those opened in 2004 by Frieder Burda in Baden Baden, and in 2007 by Frank Cohen on Wolverhampton's outskirts, are exemplary.

Both collectors have been active for 40 years - Cohen's first purchase was a small Lowry, Burda's a slashed Lucio Fontana, bought in rebellion against his father's blue-chip German expressionism collection. Each then focused his interests - Burda on postwar and current German painting, Cohen on global contemporary artists in diverse media: Olafur Eliasson, Jason Rhodes, the Chapmans.

As their collections expanded, each searched out display space. Cohen looked in London, Burda tried to build in Mougins on the Côte d'Azur, near the Maeght Foundation - even buying several Mougins-era Picassos to rebut claims that his collection was "too German" - but was defeated by French bureaucracy. Each eventually opted for a site close to his childhood home, and so transformed the artistic landscape of a familiar location.

Baden Baden, whose belle-époque hotels, thermal baths and sweeping lawns are virtually unchanged since the city's 19th-century heyday as Europe's summer capital, had history but no contemporary art until Burda commissioned Richard Meier to set a small, sparkling glass and aluminium white cube in an enclave of ancient oaks and beeches. Giant blinds control natural light, which floods an interior crisscrossed by ramps and affording spectacular, changing views of every level of the museum, the sculptures around it, the tree-fringed Lichtentaler Allee beyond. It is an ideal nature-art symbiosis: at night the illuminated Frieder Burda Museum looks like a star floating in the park; by day Meier's award-winning building allows the compelling juxtapositions and contrasts of Burda's paintings - the largest group of Gerhard Richters in private hands; key works by Sigmar Polke and George Baselitz - to be appreciated on a grand yet intimate scale.

In four years, world-class temporary exhibitions have put this tiny Black Forest city on the contemporary art map, and Burda this summer signed a borrowing agreement with Paris's Pompidou Centre.

At Initial Access, Frank Cohen has found a home for his eclectic contemporary collection in a pair of giant warehouses in an industrial park. It is a stark, edgy, slightly chilly place that gives scope to the drama of the monumental installations characteristic of Cohen's choices: Bharti Kher's five-metre fibreglass elephant coated with bindis, the Indian forehead decorations; Terence Koh's crimson self-portrait in beeswax, blood, paraffin and Chanel lipstick; a steel screen, black stage and smashed drum kit in Banks Violette's "Hate Them". This is a bold, angst-ridden, young aesthetic where art can be anything from everyday life, and the urban setting of the warehouses is a perfect backdrop.

Cohen's Chinese and especially Indian holdings are lively and well-researched - aspects that have special resonance in the west Midlands, with its large Asian population. Throughout, Cohen's taste is figurative, defiantly anti-theoretical, almost pragmatic in its emphasis on instant-impact wow-factor - his roots as a DIY salesman who made his fortune through a chain of shops is no doubt an influence. Initial Access's success lies in presenting on its own terms, in its own space, the busy confusion of contemporary art through the context of an authentic collector's vision.

Museum Frieder Burda, Baden Baden, tel: +49 (0)7221 388980; www.museum-frieder-burda.de

Initial Access, Wolverhampton, tel: +44 (0)1902 790419;www.initialaccess.co.uk