Two months ago thieves stole two Van Goghs and one Cezanne from a Rome museum. Police recovered the paintings from the thieves' apartments last week. But why steal famous paintings? Stolen paintings this famous could never be publicly displayed in a museum or rich person's home, which means they can't just be resold at Sotheby's. They may be worth millions, but how can a thief turn them into cash?
One way is to sell to private buyers. Of course, these buyers cannot display or resell the painting--they are true aesthetes, willing to buy art just to look at it. Sometimes a collector will even commission a criminal to steal a particular artwork. (This is what Italian police initially suspected, since by stealing the Van Goghs and the Cezanne, the bandits passed up several more valuable works.)
A second way is to exact a ransom from the owner or owner's insurer. Third, if the painting isn't really famous, the thief can raise money by offering the stolen canvas as collateral for a loan. Even reputable banks don't always check the provenance (record of its ownership) of items they take as collateral.
Finally, drug traffickers and other ne'er-do-wells may use paintings as a sort of international currency that is easy to transport and hard to counterfeit.