Left2Right has three interesting posts on property rights, here, here, and here. I've only read the first two (I just discovered the third), and only part of the rather extensive comments. I never thought about property rights, as such, much before, so I'm not quite sure where I stand.
I think it is pretty obvious that natural property rights have little or nothing to do with property rights in a modern society. But I do also have a strong "what's mine is mine" feeling, which is probably why I hate eminent domain so much.
On the third hand, I definitely feel that modern, capitalist economies are nothing like a free market (nor should they be), and that therefore some people will have an advantage in whatever variety of modern economic system in place, not just by things like having rich parents, but because they happen to be well-suited to this particular system. By the same token, those who end up homeless may simply be poorly suited to the system, and may have been more successful in a different system. As such, I do also feel that those who have disproportionately benefited from the system, the wealthy, have a certain responsibility to those who have not benefited from the system.
I see it this way. You have two guys, one who is good at Trivial Pursuit but sucks at Scrabble, and the other who is good at Scrabble but sucks at Trivial Pursuit. Which one will succeed or not has less to do with the two guys and more to do with what game is being played. I feel the economic systems are kind of like that. For instance, in a system that is based on natural property rights, there is no such thing as "intellectual property." Therefore, under such a system, brilliant inventors will basically get screwed when someone who is better at implementing the inventor's ideas comes along and uses the inventor's idea to get rich. In a system more like modern America's, however, it's all about having the idea, so the inventor is the one who benefits rather than the implementer. The rules of the game don't entirely determine the outcome, but they make a significant difference.
Anywho, that's how I see it right now, with my amazingly poor grasp of the intricacies of property rights.