If _12 Monkeys, and _Jacob's Ladder_ (1990) had a baby, it would be _The Jacket_.
This movie is difficult to classify, it has elements of sci-fi, drama, mystery, even romance. However, the genre details aren't as important as the story itself, and the story isn't as important as the emotional content within. This is one of those rare movies that can't really be spoiled: you could know every part of the movie, read the screenplay, and it wouldn't ruin the journey. Adrien Brody, and Keira Knightley **are** this movie.
If I could time travel to an era when video-rental stores existed, I'd put this in the sci-fi section, although, the reason I'd watch this would be for the romantic component.
What to know before going into this: if you don't enjoy mind-bendy sci-fi, you're probably not going to like this. If you want this to be a loud, action-packed popcorn flick, you're not going to like this. This movie is very subdued, cerebral, and filled with a kind of emotional beauty that is difficult to put into words without getting into maudlin poetry.
All this for a film about a guy being strapped into a straitjacket, locked in a mortuary cabinet, and time traveling to fall in love with Keira Knightley. Sounds stupid in oversimplified terms, but ultimately, it's a reminder that love is worth all the time in the world.