One of the areas I used to be really interested in was the philosophy of time travel as represented in science fiction, especially with what happens if you change your own past, and how that ties into possible physical models of the universe. So there's the Back to the Future model, the Terminator model, the Quantum Leap model, the Sliders model, and so on. The problem if we ever do manage to travel backwards in time is knowing which model actually works. Maybe I'll write more on that at some point.
Anyway, here's a funny quote from Terry Pratchett, messing around with the idea in The Last Continent:
"I can't help thinking, though, that we may have... tinkered with the past, Archchancellor," said the Senior Wrangler.
"I don't see how," said Ridcully. "After all, the past happened before we got here."
"Yes, but now we're here, we've changed it."
"Then we changed it before."
And that, they felt, pretty well summed it up. It is very easy to get ridiculously confused about the tenses of time travel, but most things can be resolved by a sufficiently large ego.