The top five list isn't really sorted, as they're wont to be - it's hard to say, objectively, how awesome one thing is in comparison to another, especially with the breadth of works on this list. All five choices are amazing, and you'd do well in reading any of them.
5. Eternal Sunshine of the Spotless Mind - Is this time-travel based? I say so. I think it is because of one particular time travel theme - that characters learn something in the span of their "travel" that applies to them in the future, even if the act of time traveling erased the act of having traveled at all. That's a pretentious way of saying "stuff happens because someone saw the past," and since this movie is great that's good enough for me.
4. Chrono Trigger - It's almost a given that it's here, but that doesn't make it any less valid. Chrono Trigger is the de-facto time-travling video game, hitting every beat that you'd want to hit - magic, technology, dinosaurs, meeting your ancestors and descendants, swords, guns, and the end of time itself. It's still my favorite overall video game experience, thanks to the gameplay and music, but the time-travel based storyline is a real delight, putting in just the right amount of "openness" in a traditionally linear experience.
3. End of Eternity, by Asimov - Did you know Asimov's an amazing writer? I just found this out, after all this time. This novel, published in 1955, doesn't feel like it's old.
2. Back to the Future Trilogy - The first work that overlaid multiple versions of the same person into popular fiction, and a great example of it. It's a fantastic trilogy that misses out on first place just because it gets a bit worse the longer it goes on - Back to the Future 2 isn't as good as Back to the Future 1 just because it ties directly in to BttF3, which wasn't great - but that shouldn't be a black eye on the series. Back to the Future 1 and 2 are really quintessential sci-fi films that are extremely accessible to the everyman, and paved the way for other light sci-fi films in a way that few things have.
1. Ghost Trick - I'd imagine this could be controversial, but this game really has everything a good story should have. Time travel really is the emotional and gameplay-based hook behind the game - change the fate of the present by doing everything you can four minutes before a given character dies. The game is constantly engaging and entertaining, with puzzle solutions that're more Monkey Island than Space Quest - that is, you can screw up, but those moments may be the best in the game instead of moments that make you wish you were playing something else. With the game available for $10 on iOS it's a must-play for anyone with the opportunity.
Memento - It's not a time travel movie persay, since the illusion and shifting of time is (mostly) in the eyes of the viewer instead of the characters. But it's a bit of meta commentary on the idea of time travel, too, in that the perception of events changes the reality of the events. It's on Netflix, Hulu, and probably everywhere else. Definitely worth a view.
Die Hard - Have you seen Die Hard? You should see Die Hard.