Hogarth Tate Britain, London SW1, until 29 April  Hogarth needs no introduction. Everyone knows what he paints - riotous taverns and surging mobs, syphilitic trollops and dandies, corrupt politicians and hearty squires, before-and-after sequences in which everything goes to hell in a handcart; vigorous moralising against the usual vices, in short, but bursting with the sight gags - the unravelling corsets, impish dogs and brimming chamber pots - of energetic John Bull comedy. His titles alone are proverbial. Even if you have never seen The Rake's Progress or Marriage a la Mode, you'll have some instinctual sense of the stories they tell and quite probably what they look like. Hogarth is Hogarthian, the Old King Cole of English pictorial satire - what more is there to say, let alone look at?  Plenty, as it turns out from this enormous exhibition, as busy as Hogarth's Covent Garden. All the classics are here plus half a hundred paintings and even more prints, from the very queer Analysis of Beauty to the final and utterly bizarre Tailpiece in which Death himself (only weeks away, in Hogarth's case) collapses in a great clutter of symbolic bric-a-brac. The curators want you to look with equal adoration upon everything in between - history paintings, theatre scenes, conversation pieces, portraits - as if he was a genius of variety. But then they also praise Hogarth (1697-1764) as 'the most important painter of his time'; alas, the untruth of that claim becomes more apparent with each gallery.  The classics are all pith and plot: he comes into money, gives up his studies and falls to debauchery; she takes to gin to ease the pain and her child ends up an orphaned prostitute. The teeming vitality of each narrative is what keeps it alive, scene after scene, otherwise you would feel depressed and hectored. For Hogarth the moralist always goes for the easy targets - the South Sea Bubble and the lottery were the subjects of his first works and he reprises the same moral in relentless permutations - youth plus unbridled greed leads to jail; youth plus unbridled pride leads to jail; unbridled lust leads to the pox (and then jail). It's a theme - the tight sequence of cause and effect - identical with his most famous pictorial strategy.  But it is Hogarth's strangeness, not his familiarity, that strikes most in this show: the curious way he throws his images together. The son of an autodidact whose attempts to run a Latin-speaking coffee house in Clerkenwell landed the family in debtor's jail, Hogarth's bitter self-reliance reveals itself in some truly unconventional compositions. Think of the portly Tory in The Election toppling backwards from his sedan chair as the bearers trip over a furious sow. Or Beer Street, planted like an advent calendar with tiny images of drunks from the gutters to the roofs. Or David Garrick as Richard III with one hand pressing desperately, as it seems, against the windowpane of the picture.  Far from being rational diagrams of the perils of sin, Hogarth's paintings are nearly always falling apart or about to explode with the build-up of messages. Pub signs and billboards, tombstones and piano scores, book titles, tapestries, pictures within pictures, sculptures that scowl down from mantelpieces, vases that seem to leer or gurn: all speak urgently from the sidelines. An overturned chair spells a row. Playing cards strewn on a fire hint the game's up. The bankrupt's marriage to the toothless crone may be convenient but the two dogs clasping paws say that it's a bestial farce.  It's generally advisable to look for the dogs or children first in this blizzard of signals. They usually form a miniature satire of the larger scenario. Or just a pocket drama in itself: a child teetering between a chair and a stack of books, one precarious foot on each; a toddler struggling to see over the brow of a table; a dog quietly peeing on someone's crucial documents. It's like a habit, a tic, this need to add more and more details to each image - to let the whole world in. But what thrives in the brilliant clarity of Hogarth's engravings nearly always sinks in the sludgy brown soup of his paintings.  There are exceptions - Marriage a la Mode is wonderfully crisp and skilful. And The Shrimp Girl, the sunshine of her immortal face so freely and beautifully painted, deserves its status as one of the great English portraits. But she isn't finished and her bright essence is all there is. Hogarth, for once, didn't get round to stuffing the picture with shellfish.  The prints, by contrast, aren't brought down by excess. They handle it with real acuity. Hogarth doesn't have to worry about pigment, tone, texture or any other longwinded painterly business. There is no pressing need to achieve a convincing illusion of life. Indeed, words don't look out of place in an etching. Hogarth can - and does - do anything he wants. The Analysis of Beauty, for instance, pretty much prefigures Surrealism two centuries in advance, its superb rendition of a country dance full of clumsy oafs and lumbering squires (Unbeauty) surrounded by a visual lexicon of eccentric items - rocks, crosses, shells, masks - being one of the most peculiar and dreamy juxtapositions of people and objects in art.  But this freedom and originality gets stalled in the paintings, as if the paint itself is in the way. Hogarth has no feeling for the substances he describes - mud can look like meat, cloth can look skin and the later canvases are as dead as an old toenail. He's apt to lose focus in a big scene, such as Midnight Modern Conversation, where you can tell what's going on from the toppling drunk to the empties on the floor - but not who's distinctive or what, if anything, matters. And for all his reputation as a judge of psychology, character and even simple likeness are not Hogarth's strength. All the portraits look queerly like him.  The paintings, however, were such runaway hits in their day that Hogarth often turned them into mass-market engravings. One joy of this show is that so many are included, for few artists better reveal the difference between drawing and painting. Horace Walpole surely had it right when he praised Hogarth as 'a writer of comedy with a pencil'; and one would not want to downplay the brilliance of the prints with inflated claims about Hogarth being more important than Stubbs, Gainsborough or anyone else as a painter.  How was it for them? We ask five visitors who went up and saw Hogarth's etchings  I'm a political arts student so I was keen to see Hogarth's work. The humour is what I enjoyed most. It's not so different from what you see in political cartoons today.  I hadn't realised he did so many paintings as well as etchings. It's such a comprehensive exhibition. I'd like to come back without the children and have a good look. My daughter Nell loved it.  This is the first time I've ever seen Hogarth's work up close and personal. I thought it was excellent. It's amazing how politically relevant his work is now.  I first saw his work on television, and when I heard the Tate was putting on an exhibition of it I had to see it. His attention to detail is amazing. The portraits are just so clear.  Absolutely fabulous! There is so much to take in. Totally rumbustious stuff. I'm such a big fan of his work.
Art: Forget the paintings - the genius of William Hogarth lies in in his prints says Laura Cumming.