Paul Cézanne's Boy in a Red Vest is an outlaw, a fugitive from justice. This lovely painting was one of a clutch of Post-Impressionist works seized by armed robbers earlier this month from a private museum in Switzerland. The paintings appear to have been stolen “to order”. The Cézanne may now be hanging on the wall of some criminal connoisseur, the prize exhibit in a private art gallery with only one visitor.

At the same moment that art thieves were breaking into the Bührle museum in Zurich, the British art dealer Anthony d'Offay was preparing to hand over his £125 million collection of art to the Tate and the National Galleries of Scotland: 725 works by some of the greatest artists of modern times including Warhol, Beuys and Gilbert & George.

That astonishing act of generosity is the single most important development for British art galleries in a generation. D'Offay does not demand to see his name on the gallery door; he wants to receive only what he originally paid for the artworks, a tiny fraction of their current value. It is impossible to calculate how many millions will now be able to enjoy the collection, far into the future.

These two events, one criminal and one philanthropic, may seem to have nothing in common: one is entirely selfish, the other spectacularly selfless. The pleasure of wandering through art galleries as a youth was, for d'Offay, the “defining experience” of his lifetime. He wants to share that sort of experience with as many people as possible. The criminal, by contrast, prefers to hoard the pleasure to himself, alone and in secret, or else wring maximum value out of it on the black market.

The art thief and the art philanthropist are at opposing moral poles of the same impulse. Both appreciate that art is the ultimate acquisition, the essential validation, with the power to transform, inspire and uplift. In the most twisted way, the art thief is also venerating the power of art.

Art robbery is as old as art, but it is a most mysterious business. Some $6 billion worth of artworks are stolen every year, according to Interpol, making this the fourth-largest criminal industry in the world after drugs, money laundering and weapons dealing. Most art thefts go unsolved.

Although too many art galleries are still shockingly ill-protected, stealing art is not an easy task. Selling stolen art is even harder, displaying it almost impossible, and the more famous and valuable a stolen painting is, the harder it will be to fence. There are much easier ways to make a criminal living. So why do crooks steal art, and buy stolen art, instead of some other commodity that is easier to filch, hide and sell? The answer, surely, lies in the nature of art itself.

The image of the crooked art-lover is a staple of popular culture, from the Penguin's art-lined lair in the Batman series to The Thomas Crown Affair. Goya's portrait of the Duke of Wellington was stolen from a London gallery in 1961. In the James Bond film Dr No, which came out a year after the theft, 007 reaches Dr No's island lair and does a double-take when he spots the painting on the wall: “Sho thatsh where that went,” says Sean Connery.

(In reality, the Goya was probably stolen by a former bus conductor in protest at the expense of his television licence; he kept it four years and then handed it back by leaving it in the left-luggage office at Birmingham New Street station.) Investigators say that most art thefts are committed to extract money from insurance companies, for ransom, or as collateral for other criminal activities such as drug dealing.

Yet while the Dr No figure is part-myth, there are undoubtedly examples of art theft to order. A man suspected of stealing two paintings in Brazil last December told investigators that they were destined for a Saudi collector. The theft of the Mona Lisa in 1911 was commissioned by a French art forger who planned to make counterfeit copies and sell them as the missing original.

In other cases of art crime, aesthetic judgment seems to outweigh mere profit. In 2003 a stunning gold-plated salt cellar by Cellini was stolen from a Vienna museum by an alarms expert who had studied sculpture as a youth: he kept the trophy under his bed for two years. The Victorian master-thief Adam Worth (the model for Conan Doyle's Professor Moriarty) stole a Gainsborough portrait in 1876, and kept it for 20 years in order to “worship its grace and tender beauty in the still watches of the night”.

Many art heists are clearly the work of amateurs, but some plainly involve planning, discernment and even critical judgement. The thieves who raided the Bührle gallery left behind the most valuable artworks, reflecting either incompetence or their employer's personal taste. When robbers stole 13 paintings from the Isabella Stewart Gardner Museum in Boston in 1990, they appear to have been following a “shopping list”, stealing some paintings, including paintings by Vermeer, Degas and Manet, but leaving others. There has been speculation that a Boston crime boss, James “Whitey” Bulger, may have been behind the robbery: the paintings have never been recovered, and Bulger is still on the run.

Anthony d'Offay represents the opposite extreme of art collecting to the Dr No figures, real and fictional. In a way, the two symbolise distinct and often competing strands within art collecting: the impulse to possess beauty versus the desire to share art with the widest possible number of people. Many collectors regard their artworks as a private pleasure, or mere investment; d'Offay saw his, rightly, as a public benefit.

Cézanne himself once observed: “I am more a friend of art than a producer of painting.” Art has no better friend than the hoarder of rare and beautiful things, who collects in order to give away.

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