This year, though, it almost seems that controversy has become a prerequisite for artistic success. The shortlist announced this week includes an artist who had a micro-camera inserted into her orifices to make videos of her internal organs; an installation artist who pickles sheep and sharks in formaldehyde; a multi-media artist who bought a racehorse and entitled it "A Work Of Art". The fourth artist on the list, an abstract minimalist painter, who once would have caused raised eyebrows, seems absurdly conventional by comparison.
The arts are awash with prizes. There are more than 200 book prizes alone; there are theatre, film, music and dance awards. Most of them have glamorous awards dinners and big cash prizes, and confer a fleeting fame on the recipients. None casts as long a shadow as the Turner Prize. None has so profound an aesthetic effect on the art form it promotes.
To understand why, one has to appreciate the power and influence of the institution that is inextricably linked to the Turner Prize, namely the Tate Gallery and its director, Nicholas Serota. The Turner Prize was set up by the Tate's Patrons of New Art in 1984. The Patrons of New Art is a group of fundraisers for the Tate that helps to buy new works of art. Though nominally their prize, all the decisions that count are taken inside the Tate. The Tate puts on an exhibition of shortlisted artists every October. It hosts the dinner where the prize is awarded. Mr Serota and the Tate trustees choose the jury. Mr Serota chairs it.
Channel 4, as sponsors, put up the pounds 20,000 prize money and can thus broadcast the prize dinner. But the influence of the Tate and, by extension, Mr Serota is paramount. The shortlisted artists get to have their work exhibited at the Tate, the foremost modern art gallery in Britain, and possibly in Europe, with the result that the financial value of their work is enhanced, as are their reputations.
And they have significant patronage too. Mr Serota is the most powerful gallery director in Britain. He is in charge of the Tate, the Tate in Liverpool and the Tate at St Ives, and will run the new museum of modern art at Bankside, planned to open for the new millennium.
The Turner Prize is the most visible and most hotly debated expression of contemporary art. It makes a public statement about what is important, what is aesthetically valuable and what is at the cutting edge in contemporary art.
With that in mind, the aesthetic philosophy of Mr Serota, and of his fellow jurors, is of some importance. Their championing of artists such as Damien Hirst (shortlisted twice), who pickles sheep and sharks in formaldehyde, or Rachel Whiteread who made a cast of the interior of a terraced house, or Mark Wallinger who buys a racehorse and labels it a work of art, gives respectability as well as notoriety to artists who otherwise may not be legitimised.
Serota and other key gallery directors are confident that in so doing they are both encouraging and reflecting the artistic direction that talented young people are taking. The young are engaged with computers, with film and with video. Art is now multimedia. And the change is a global one. At last month's Venice biennale it was hard to find a national pavilion that did not have a video installation or a wall of photographs.
The Turner Prize has had a substantial role in both reflecting and effecting this change of attitude, a change that is also reflected in the art schools where a video camera is given equal status with a canvas. The Turner prize has become the champion of the conceptualist, of the stone circle or the bed of rice which provokes some spectators to psychological awakenings and others to cry rubbish.
The Turner Prize also likes to maintain the place of wit in art. Damien Hirst is cited as a witty artist by this year's jurors. And many of the installations one sees in the Tate are humorous. Not for nothing are attendances at the Tate higher during the months when the Turner Prize exhibition is on. The Turner Prize and the Tate should get its due credit for provoking a genuine debate about contemporary art and attracting new audiences into the art gallery.
But there is a downside to the Prize's championing of the conceptualists, which the Prize's detractors are not slow to point out. Painting, of the representational and figurative rather than abstract variety, rarely features on the shortlist, quite an irony when one considers after whom the prize is named. And so one has the curious situation that some of Britain's best-known figures in modern art, people like Lucien Freud and Paula Rego, have not won the Turner Prize. They are, of course, both figurative painters.
Last year, the Jerwood Foundation, an educational charity, set up a painting prize to rival (and financially exceed) the Turner Prize. One of the judges was Judith Collins, assistant keeper of the modern collection at the Tate Gallery. In a telling revelation, she says: "I was pleased to have been a judge last year as it was a great learning experience for me. I saw evidence of painters' works that hadn't crossed my desk before at the Tate."
One of this year's Turner jury, the art critic William Feaver, defends the general exclusion of painting. Painters, he says, tend not to have really made a splash until they are over 50, above the age limit for the Turner Prize. David Hockney, among others, might dispute that assertion.
It is significant that one of this year's shortlist is the multimedia artist Mark Wallinger. He, in fact, paints horses, but knowing the Turner climate as he does finds it necessary to justify this by saying it is a political act, "a preoccupation with the world of horse racing as a vivid microcosm of British society in which issues of class, breeding and money were particularly focused".
But if the Turner Prize does, as its critics imply, go out of its way to be controversial, to choose artists whose work is bizarre but by its very nature ephemeral (Rachel Whiteread's house was demolished by the local council), does it matter?
The Prize's defenders, which include nearly all of the contemporary art establishment, argue that the history of modern art over the past century has been one of continual challenge to conventions. The new must shock and when the Turner Prize ceases to shock it will have outlived its usefulness.