Those who've been watching LOST lately are probably thinking a lot about paradoxes and what-ifs. My personal favorite paradox is the compass. Alpert gives Locke the compass c. 2004, but Locke gives Alpert the compass (via time travel) in 1954. If Locke got it from Alpert, and Alpert got it from Locke, where did it come from?
To help explain, here's a nice humorous quote dealing with time travel and paradoxes:
If the Universe came to an end every time there was some uncertainty about what had happened in it, it would never have got beyond the first picosecond. And many of course don't. It's like a human body, you see. A few cuts and bruises here and there don't hurt it. Not even major surgery if it's done properly. Paradoxes are just the scar tissue. Time and space heal themselves up around them and people simply remember a version of events which makes as much sense as they require it to make.
Thus spoke Douglas Adams, so it must be true.