this recent article and Op-Ed from the New York Times brought it to the forefront.
The most famously contested collection in a museum are the Elgin Marbles in the British Museum, removed by Thomas Bruce, Lord Elgin, from the Acropolis during the early part of the 19th Century. The trouble is, of course, that although Elgin may or may not have obtained permission from the Ottoman Empire, said permission does not have the support of the Greek government. In fact, the Greeks very much want them back.
I see both sides of the issue. The marbles are unquestionably Greek, and certainly represent a great chunk of Greek history. However, had Elgin not absconded with them when he did, they might very well not exist. The Turks stored gunpowder in the Parthenon, which had already gone kaboom once before. So, 200 years ago, the marbles became a piece of British history, controversial though they are.
I have a bit more of a bias when it comes to Italian antiquities, likely by virture of having lived there Not that I don't believe they represent a part of Italy's history--on the contrary. The trouble is that Italy just has so much history. The amount of art there is staggering, but the funds necessary to maintain are limited (it's a country, after all, not a museum). Additionally, a great amount of the art is exposed to the elements, which is frustrating especially in the cases of Pompeii and Ostia Antica, when nature did such a wonderful (if tragic, in Pompeii's case) job of preserving frescoes and mosaics (like the fantastic Cave Canem, or "Beware of the Dog" fresco, above).
So. That's my rant. Of a sort. I do recommend reading the Op-Ed, which is about museum treatment of artifacts of contested provenence, and is quite good. If anyone is interested in additional information on this topic (say, for example, the Italian restorations of Leonardo's Last Supper and Michelangelo's Sistene Chapel Ceiling, or who really made the Venus de Milo), let me know! I've got a ton of this stuff rattling around in my head.