Timestripper

You play the character Shinji Nakayama a high school student who has a bad reputation of cheating on his girlfriend, Michiyo Sakagami.

The story starts when your "habit" is eventually found out (again) by your girlfriend, of which you start to fight and end up breaking up. In the middle of your 'sobbing', a girl pops up out of nowhere in your room. It appears she's from the future, with personal reasons that has to do with your present love-life situation. After that, the story is in your hands...

[From MobyGames]