Without a doubt this Sonic game, and since no one has mentioned it.
Get it from PS3/PSN shop. "With the excellent enhanced features: 16:9 Widescreen narrative, HD, Tails unlockable, Sonic 2 spindash physics optional along with the original Sonic CD physics, both US and Jap/EU soundtracks included and incredibly cheap to purchase. A game heavily based on exploration with the amazing time travel gimmick. Excellent music and great replay value. Thoroughly enjoyable. 10/10."
This had time Travel and Multiple endings in 1993 before Chrono Trigger 1995.
It's 4.99 to boot.
Sonic can travel to the past and future of each Zone in the game by running at top speed for a set amount of time. The goal in each stage is to destroy a machine that the antagonist, Robotnik "Eggman", has placed in the past in order to conquer the future. The future of each Zone will change from "bad" (default, ruined future) to "good" (lively and happy) if the machines are destroyed.
