Watch Me Move: The Animation Show, Barbican Art Gallery, London

An art gallery is, by nature and precedent, not a place for showing films, so it was bold of the Barbican gallery to attempt a giant survey of animation from the past 150 years.

No cinema could have done it: there are more than 100 examples here, ranging from the work of the Lumière brothers through early Disney to The Simpsons, Japanese anime and CGI. Yet this isn't only about the march of technology. Watch Me Move shows that the moving force in animation is the power of imagining.

The exhibition title comes from a sequence from a short made by Winsor McCay 100 years ago. It's simply a parade of hand-coloured archetypes – prince, clown, dragon, princess – each of which demonstrates the tricks of their maker's relatively novel trade, stretching, squashing and morphing comically into other forms. The animation may strike us now as basic and repetitive, but its effect is far from simple. Harnessing the cyphers of childhood stories, McCay's little entertainment taps into the collective unconscious. In their comings and goings from and into nowhere, too, these storybook figures assume the character of our dreams – a recurring feature in this absorbing show.

The selection is divided into loose themes – apparitions, superhumans, fables, visions – set over two floors, though you need a good three or four hours to do justice to it all. The Berlin-based design company Chezweitz & Roseapple has divided some of the space into cubicles, screened with black net, with nylon filament doors that drape over you like cobwebs as you pass silently through. Double-sided screens hang on the net walls, so you get a double chance to see some things. Further on, a room showing a film on each wall contains padded booths with directional speakers, so you're never bothered by overlap. The largest room encourages you to lounge on leather pouffes wearing headphones. Apart from some slightly whimsical captioning, the layout is helpful, and makes you want to linger.

Included in the first section are experiments with photography and physics, as well as early comic marvels such as The Skeleton's Dance, created as part of Disney's Silly Symphonies of 1929. It makes a marked contrast with the Lumière brothers' own dancing skeleton, Squelette joyeux: same theme, younger technology.

The thematic approach means that recent work can be viewed alongside archive items: McCay's Gertie the Dinosaur (1914) with Steven Spielberg's Jurassic Park (1993), while in John Lasseter's two-minute short for Pixar (1986), two Anglepoise lamps, one big, one small, sweetly assume the character of a dinosaur parent and child.

On a large scale, though, the piece that held me longest was Run Wrake's 2005 film Rabbit, which spookily appropriates 1950s educational picture-book illustrations (complete with captions such as "girl", "boy", "tree"), to spin a macabre tale of two children who, on cutting open a rabbit (don't ask), discover a genie that can turn base objects into jewels. Fabulous stuff, that, alas, won't be showing in a cinema near you any time soon.

Until 11 Sep (0845 120 7550)