But they'd like to

Slate has a story by Jacob Leibenluft about the Indian space program (no, that's not a joke):

India launched an unmanned lunar orbiter Wednesday morning, marking the nation's first mission to the moon. The orbiter will, among other tasks, attempt to identify possible uranium deposits on the moon. Can India claim whatever uranium it finds up there?
No. The Outer Space Treaty—which was signed in 1967 and has been ratified by almost every country with a space program—is very clear that "outer space, including the moon and other celestial bodies, is not subject to national appropriation." (That's why the American flag placed on the moon by Buzz Aldrin and Neil Armstrong was a symbolic gesture rather than an effort to claim the moon as U.S. territory.) So even if the mission—which is being conducted with the cooperation of NASA and other national space agencies—manages to find some uranium deposits, no country would be able to claim ownership. For that matter, it's highly questionable whether there are any property rights at all in space. As for those deeds for lunar land you can buy online, the legal consensus suggests they'll never hold up in court.
If a country—or a private company—were to try opening a mine on the moon, it would be stepping onto uncertain legal ground. The Outer Space Treaty is silent on the question of extracting natural resources in space, and legal experts differ over what language mandating "free access" to all areas of space might mean for mining. Likewise, the treaty prohibits "harmful contamination," and this restriction might cause thorny legal issues if extensive mining operations were thought to raise environmental concerns.
Another international agreement, the so-called Moon Treaty, which was adopted by the U.N. General Assembly in 1979, is a good deal clearer. It states that "the moon and its natural resources are the common heritage of mankind" and specifies that those resources should only be exploited under the oversight of a new international regime. But the Moon Treaty was never accepted by any of the traditional space powers, like the United States or Russia. India is among the 17 countries that have signed the Moon Treaty, but it never fully ratified the agreement.
Some space-law experts contend that there may be a precedent for mining: Both the Americans and the Soviets took moon rocks back to Earth, and no one objected. More probably, any attempts to extract uranium or the potential energy source helium-3 would spur a new round of international talks. In that case, countries might look to agreements surrounding the high seas or Antarctica for guidance. In the case of Antarctica, rules on land use are determined by the few dozen nations that have signed onto a special Antarctic Treaty. In the 1990s, those countries agreed to ban mining on the continent until at least 2048. By contrast, the International Seabed Authority was set up in 1994 to administer claims by companies seeking to mine in deep-sea areas that lie hundreds of miles offshore; the United States, however, hasn't ratified the Law of the Sea Treaty that would make it part of that organization.

Rico says it's all pretty funny, because it's going to be a long damn time before India can actually put an astronaut on the moon to bring anything back, anyway...