I've always been vaguely fascinated by time travel stories. There's just something about the outright subversion of linear storytelling, combined with the intricate logical knots you often end up with, combined with the fun of poking through the story a second time to tease out paradoxes, that really just makes me really happy.
The trouble, unfortunately, is that really good time travel stories are kind of hard to do, and thus pretty rare. My favorite example of a time travel story is an unlikely one: Bender's Big Score, the first Futurama movie. Not only was it a damn funny movie, not only was it a really well done time travel story, but it also had Fry/Leela romantic fluff. How could I not like it? Then, too, as far as I can tell the movie remained logically consistent, or at least believably so. (One of these days I'm going to watch it again with a pen and paper, and really check that they didn't create any paradoxes. When "one of these days" actually comes around, I'll be a pretty busy guy.)
There are three main schools of thought about how paradoxes are resolved with time travel. The first is the "yay special effects" school of thought, not generally seen outside of movies. With this approach, if you were to go back in time and kill your grandfather, you'll start to fade out dramatically, and maybe have a few minutes to reflect upon your folly as your body parts start to disappear. The second is the No Paradoxes (reactive) approach, in which any time you try to change the past, something else happens which conveniently undoes whatever it was you were trying to accomplish. A good example of this is the (horrible, recent) movie version of The Time Machine. The third, and most logically sound, is the No Paradoxes (proactive) approach, in which you can't change the past, because you were already there, so whatever you did has already happened. This one doesn't play well on the silver screen, so it's the least known of the three.
I know I said that the Futurama movie was my favorite example of a time travel story, but it can't hold a candle to the greatest time travel story ever, All You Zombies by Robert A. Heinlein. It is about a person who is his own father and mother. Think for a moment about the genealogical implications of that, and you'll realize why RAH is one of the greatest sci-fi writers ever.