Contemporary art: You cannot be serious

If I did theatre, I'd do fun. I'd do things like Puppetry of the Penis, The National Theatre of Brent, The Lion King, Stomp! – and I'd have to enjoy it, at least from time to time. That's the deal when you're a theatre critic. You're broad. You can't be holding out constantly for Samuel Beckett or Wallace Shawn. You have to throw yourself into the world of low entertainment, even if you feel a bit ridiculous, even if you have to fake it. That's the job.

If you want to be a full-time highbrow, be an art critic. We're always terribly serious. It's not just the general lack of Stomp! Pretty well everything in contemporary art is more egg-headed than anything on the contemporary stage – you just have to read our accompanying leaflets and catalogues. No exhibition comes without its quasi-academic essay. A strange world, if you think about it, and a quite recent development. But it wouldn't feel respectable any other way.

Or perhaps I'm missing something. Perhaps we do have fun in contemporary art, and fun of a pretty simple kind – it's just that we're not straight about it. What about Carsten Höller's Test Site, the spectacular helter-skelters erected in Tate Modern a couple of years ago? What about the reconstruction of Robert Morris's Bodymotionspacesthings, at Tate Modern again, on which people have been happily seesawing and tumbling?

Of course, we don't call these things fun. We call them interactive installations, and we say that they raise important issues about all sorts of things. But people do seem to enjoy them in a perfectly straightforward way. As experiences, they don't seem very far from the funfair or the playground.

And now here I am, half a mile up the river, at the Hayward Gallery, and I'm going around "Walking in My Mind: Adventure into the artist's imagination". There are exhibits by 10 artists, and each one is an invitation into their own mental world. Some of them are literal interior spaces, where you go inside and maybe get a little lost. Rabbit holes? "Adventure" would possibly like us to think of Alice and Wonderland.

True, one of the works comes with parental guidance, warning us of its explicit obscenity. And "Walking in My Mind" doesn't actually incorporate a boating pool, which last summer's Hayward show did. But it does have galleries that are a bit like a maze, or a hall of mirrors, or a ghost train, or a planetarium. A holiday entertainment for the whole family, then?

Try the dotty world of Yayoi Kusama. The Japanese artist, 80 years old, has spent much of her life in psychiatric hospitals. Her work is full of spots, and here her installation has rounded blobby forms, resembling giant skittles or chicken drumsticks, and spotted white-on-red, like cartoon toadstools. Their images bounce around a mirrored room, making it hard to distinguish reality and reflection as you walk among them. They also occupy an outdoor fake-grass area like alien growths.

Or enter deep into a voluminous network of caves, constructed by the Swiss Thomas Hirschhorn wholly from cardboard and parcel tape. You have to clamber and explore. They really are quite atmospheric, for a DIY job. Their walls are adorned with books (philosophy, international politics), themselves attached to dynamite belts made of silver foil, and there are life-size silver-foil figures standing around, and oversize books, too. Lascaux meets Tora Bora?

You can be ensnared by a web created by Chiharu Shiota (Japanese again): a labyrinth of cat's cradles of taut threads, with at its centre a group of huge white bridal gowns, trapped in a dense thicket. What spider laid this layer? You can be boggled in a circular projection room staged by Pipilotti Rist (Swiss again). Images of body-parts, isolated and magnified, float and swim around its darkened walls like planets – a foot, a mouth with its tongue moving, an ear, a penis.

There are other exhibits that don't take you into an engulfing interior, but offer something more like the working parts of a mind, set out. Bo Christian Larsson (Swedish) accompanies you up a flight of stairs with a cast of enigmatic surreal archetypes. Jason Rhoades (US) does a horrible creativity joke, a bloke shed, full of gadgetry, woodwork and porno pictures of penises. (This is the one advising parental guidance.) Keith Tyson (UK) shows walls of his extraordinarily diverse pictures, each one like a mental/visual experiment.

So, it's a kind of concept, and it sort of works. "Walking in My Mind" offers some moderately estranging stuff (too many of its effects involve making things big). But it seems to me a divided project.

I won't begin to tell you what it says about it in the catalogue, but you can probably guess – madness, philosophy, penises – that there's an undercurrent of the disturbing and the pretentious almost everywhere. Of course: the disturbing and the pretentious are always around the corner with contemporary art, and too often they make up for a lack of wonder.

"Walking in My Mind" has its immersing exhibits, and its ideas about going into the mind, and its talk of adventure. It keeps promising wonder, a vista of dreamscapes. It doesn't deliver. There's a glimpse in Hirschhorn's caves and in Rist's organ-arium. But there's not enough to truly mystify or disorient or amaze.

And what would that be like? Try this. Last year, my memories stirred for the Crooked House that once stood in Battersea funfair. What a magical structure it was, as I recalled it – its rooms with randomly angled walls and floors, its stairways with every step on a different slant, with beautiful period furnishings and incidental peepshows containing baffling illusions.

I wondered what had become of it, and Googled, and found that rather than having been destroyed when the funfair was closed, it had been bodily transported and could still be experienced at the family amusement park at Dymchurch on the south Kent coast. (Dymchurch, incidentally, where Paul Nash did some paintings in the early 1920s). I went.

False fond memory syndrome! What a disappointment and a mistake. The Crooked House was a small boxy building, with a downstairs and an upstairs, a couple of empty rooms in each, which had been simply jacked up from one side, giving everything the same slope. There were bad cartoons painted on the walls. It was a bit wobbly to walk around. There were no complications or refinements at all. Presumably childhood had added most of the magic. So where to find the adult version of this experience?

Well, where else but in contemporary art? It can deliver some very classy spectacles and illusions. This is one of its specialities, in fact. "Walking in My Mind" gives a hint, only a very weak hint, of its powers. But think of the grand optical mirages devised by James Turrell or Anish Kapoor, where the empty air becomes a solid surface or a cavity opens out into a depthless void.

Think of Olafur Eliasson's The Weather Project, the indoor sodium sun, or Antony Gormley's Blind Light, the consciousness-dissolving fog box. Think of story-telling installations, like Louise Bourgeois' haunted chambers or Annette Messager's raging oceans of blood-red silk. (Both the Gormley and Messager have been at the Hayward). And this list could go on.

Now, when I'm in highbrow mode, I tend to look down on these things, and especially if they're coming on in highbrow mode too. But take them at face value, as highly imaginative entertainments and experiences – mind-blowing, spooky, fun – and how effective they are.

These art works are a new and distinctive genre of our turn of the century. They don't have a collective name. I doubt whether they'll be properly recognised. No impresario will ever put together a Contemporary Art Wonder Park, consisting entirely of such delights. Too vulgar. Too exposing of what's really going on. It wouldn't need either catalogues or critics. But it would work brilliantly.

'Walking in My Mind: Adventure into the artist's imagination', Hayward Gallery, London SE1 (haywardgallery.org.uk, 0871 663 2500), until 6 September