A furry tea-cup, a shiny vinyl typewriter, a bicycle wheel mounted on a kitchen stool, a basket-ball hanging in salt water. What do they have in common? That's a question the Hayward's latest show doesn't quite answer.

Picasso's painting Still Life with Pitcher and Apples shows a piece of sexed-up tablewear. The jug is made woman, its texture rendered as if it was the heavy flesh of one of his neo-classical fatties, its slow curves and protuberant bulges formed into suggestions of neck and breasts, or waist and buttock. But these transformations are quite tactfully done, just a slightly more explicit version of the sort of body-metaphors that are present in much old still-life painting. A still life it undoubtedly remains.

Meret Oppenheim's surreal Object is another piece of sexed-up tableware. Its tea-cup, saucer and tea-spoon are made woman, all furled with a covering of fur, giving the receptacle maybe a pubic hairiness, certainly allowing all sorts of connections and jolts to happen between smoothness and roughness, use and ornament, the domestic and the erotic. But, of course, though Magritte might have painted a furry cup, this isn't a painting, it's a real object. And is it still a still life?

How much does it matter that its body-metaphors are not got by visual persuasion, but by a straight juxtaposition of materials and their associations? Or that there's no real tradition of still-life sculpture for it to find a place in? And then, how about Duchamp's junction of a bicycle wheel and a kitchen stool, or Warhol's painting of blank rows of labelled soup- tins, or Oldenburg's soft typewriter made of shiny vinyl, or Jeff Koon's basket-ball suspended in a tank of salt-water - are these things still lifes too?

I'm not sure I know how to answer those questions, and I probably wouldn't have asked them or thought they were worth asking if it weren't for "Objects of Desire: The Modern Still Life", an exhibition organised by the Museum of Modern Art, New York, which now fills the whole of the Hayward Gallery in London. The still life - from Cezanne to now - is the plan, and naturally there's a lot of work where the genre-label is unarguable or at least arguable - Cubist still lifes, Surrealist still lifes, Metaphysical still lifes, Purist still lifes, Matisse still lifes. Anyone who just wants painting has more than enough to fill an afternoon.

And then there's a lot besides: for example, all those works mentioned above, ready-mades and found or altered objects, Pop art reproductions, neo-Pop constructions. For the range and abundance of its contents this is certainly a show to be seen. Indeed, by its eclecticism, which allows it to include almost all the big names and chapter headings of the century (abstraction being the big exception), it can extract from the "still life" rubric what's virtually a little history of modern art.

But even a little history of modern art is a large and complicated thing. To praise the exhibition as a whole for its range isn't wholly praise. This is not a permanent collection, to be visited and revisited over the years. And a show where the viewer is asked to turn on an aesthetic sixpence at every corner (for such is the history of modern art) can't but encourage inattention to individual exhibits, in favour of a gliding wonder over the kaleidoscopic array, the great party that's been got together. All these things - all still lifes? Well, fancy! What that? And that too?

"Objects of Desire" has too much of an eye on itself as an embracing spectacle. It offers a drama of the one and the many: the one genre and its many, many different examples, with the anthologist's glee at the sheer variety of things that can (at a pinch) be brought under one roof, which tends to reduce everything to being one more example. There's also a drama of estrangement. Rather as Magritte, in one of his paintings here, gets a mind-bending charge from labelling a leaf as "le table" and a jug as "le fruit", so there's a pleasing strain in looking at (say) one of Jasper Johns's flag-paintings, also here, and trying to call it "la nature morte" - ooh, a just-about, sort-of, stretch-the-point still life. It doesn't quite figure, and that's the kick. And so what?

It's not a matter of defending the purity of the genre against intrusions, or of dissing the Jasper Johns (though the particular flag-painting shown isn't painted so intensely as some other versions). It's simply that it's hard to see what is gained by putting it in hopeful dialogue with pictures by Gris or Mir or Leger or Morandi. More or less ingenious connections can be drawn, as can be drawn between anything and anything. A very general heading of "everyday objects removed from their everyday setting" can be applied to every work in the show, from Cezanne's tabletop landscape to Warhol's "Brillo Boxes" (if, that is, you're prepared to be very flexible with the meanings of "everyday" and "removed"). But a lot of big differences get suppressed in the process.

I think that's the object, though. The idea is to smooth art history out. I don't deny that following the course of still life turns up some good history too, particularly around Cubism. Cubism was largely invented on still life (the easiest subject to have your pictorial way with). It was cubist still life that invented collage (the bits and pieces of real stuff that Picasso and Gris started to stick to their paintings). It was Cubism that invented true still-life sculpture (like Boccioni's bronze Development of a Bottle in Space). And, if you will, these things can be seen to segue into various lines of found-image and found-object work.

But there it seems more important to insist that what Duchamp did and what Warhol did really were ruptures, and that what's presented here is an essentially emollient history of modernism. Still life is being used in this capacious way to make things hold together. The approach is very characteristic of the New York Museum of Modern Art, which has always sought to subdue both conservative fears and radical hopes that 20th-century art has exploded in all directions, in favour of keeping the show on the road, as a lively but unbroken relay of bright ideas. This is friendly, but it's false.

What's more, this approach tends to minimise the main benefit that any anthology offers: turning up obscurities. The show is so keen to bring all the famous names under its umbrella, to prove that still life is a big central story of modern art, that it doesn't have much room for real finds. But there are a few good ones (relative to my own ignorance, of course), mostly in the later rooms. There's Robert Therrien's perilously stacked pile of giant-sized dishes and bowls, for instance, and Mario Merz's very simple, joyful, harvest-festival-spirited Spiral Table - a spiral of metal trellises heaped with fresh fruit and veg.

And the exhibition has a lovely end in Wolfgang Laib's Milkstone, a large low tray of pure white marble, filled up to the very rim with milk, so that what's solid surface and what's liquid surface tension are held in nearly indistinguishable stasis (though an old Eric and Ernie routine involving kettle drums comes to mind too).

Perhaps, by this point, most viewers won't be thinking about "The Modern Still Life", in all its likely and unlikely guises, at all - just treating the show as a generous miscellany from which to take their pick. Really, that would be the best starting position too.

10am-6pm daily (Tue/Wed to 8pm), until 4 January, Hayward Gallery, SBC, London SE1. Tickets pounds 5. Booking: 0171- 960 4242. Sponsored by BMW