Space policy expert Rand Simberg has an interesting article in the New Atlantis on the need for private property rights in space:
Space contains valuable resources. These provide a compelling reason for entrepreneurs, investors, and governments to pursue space exploration and settlement. Asteroids are known to be rich in valuable elements like neodymium, scandium, yttrium, iridium, platinum, and palladium, most of which are rare on Earth. Because of the high price that these minerals command, harvesting them from space could possibly justify even very costly mining expeditions....
Despite the progress in technology, and the appeal of valuable resources, space settlement has been hampered by the lack of a clearly defined legal regime for recognizing property rights in space under current U.S. and international law. There is in fact some slight internationally recognized legal precedent for retaining ownership of resources mined in space, as lunar samples returned to Earth on both U.S. and Soviet missions (the latter robotically) have been exchanged for other tokens of value. But actually owning the portion of the celestial body from which the resources are harvested — as in a traditional mining claim — is more problematic. Without legally recognized rights to buy, own, and sell titled property, it is difficult if not impossible to raise capital to develop land or extract the resources it holds. Property rights have long been considered one of the pillars of prosperity in the modern world, and their absence in space — due to the contingencies of the history of international law during the early space age — partly explains why we have not yet developed that final frontier.
I briefly advanced a similar argument in this 2007 post, where I also noted that former astronaut Buzz Aldrin, the second man to walk on the Moon, is a longtime advocate of private property in space.