A pair of Democrats in the US House of Representatives have recently proposed the Apollo Lunar Landing Legacy Act which would establish a US national park in the areas surrounding the six Apollo landing sites. The Outer Space Treaty of 1967 prohibits any nation from claiming ownership of parts of celestial bodies, so it seems to me that such an act would be of dubious legality. The larger point, however, merits some additional examination.
About fifty years of historical artifacts have now accumulated on the Moon and Mars. From the first man on the Moon to the first machine on Mars, these sites represent some of the greatest achievements of the Cold War-era world. The isolation of space has protected them thus far (Neil Armstrong's footprints have likely been undisturbed by time). But with increasing national and commercial interest in space, how do we protect these relics in the future? The same treaty which prohibits ownership of the Moon bans tampering with other nation's equipment there and elsewhere, so there is at least some legal framework here. It'd be hard to extend ownership to things like footprints, though, and even harder to enforce.
Suppose a private company in Russia or China develops a small commercial Moon rover. If they are looking for the maximum publicity, sending it to drive around and photograph the Apollo 11 landing site wouldn't be the craziest idea in the world. In the process, priceless American history could be destroyed. Given the strained relations between the US and these nations, would China or Russia really intervene? And, if they didn't, would the UN (given ultimate authority by the Outer Space Treaty) risk making an international incident out of it? Copyright and identity theft, as well as email spam, are prevalent in these countries, yet international pressure seems to have little effect.
Perhaps space will not afford history the permanence we once thought it might. Instead, like on Earth, subsequent generations will leverage and re-purpose our common history for their advancement. Like the Great Pyramids of Egypt were striped of their limestone facades, we may end up damaging our legacy for a fleeting gain.