All the games were mentioned before, but a few games I liked using time-travel in any way:
Lost Vikings - A fun puzzle/platformer with 3 characters you had to constantly switch through (made easier with a 6-button Genesis controller). One that can jump and bash walls down, one that has a bow and a nigh-useless sword, and one that has a shield that acts as a parachute as well. The sequel replaced the sword with a robot arm that can be used to swing across chasms. It is also a Blizzard (Formerly Snowblind, who also did Rock n' Roll Racing) game, and they are even in Uldaman.
Turtles in Time - Even though I preferred the 3rd game for the NES, it was still fun.
Space Quest IV - You travel between Space Quest games, not time-lines. Though that one part in Space Quest I is pretty hard because you need to be perfect in your timing.
Chrono Trigger - You could manipulate different things, and get different endings based on when you killed the final boss.
Final Fantasy VIII - Yes, I did like it. And it makes such a nice time loop at the end, plus I love "Eyes On Me". Not to mention living through (Spoiler)Squall's father, Laguna's life.(/Spoiler)
World of Warcraft - Anything involving the bronze dragonflight. Also the final scene of the Death Knight starting area.