Chrono Trigger

Chrono Trigger is an RPG developed and released by Square for the SNES, and later ported to the Nintendo DS. It consists of real-time decision-making much like the Final Fantasy series (players can be attacked while choosing options in battle), and incorporates original concepts throughout the game. Most notable, hinted by the title, is time travel which the story progresses through and becomes entwined with.

Story
Crono, the main character, wakes up one day ready to go to the fair and have fun with his friends Lucca and Marle. Unfortunately, Lucca decided to build and show off a teleportation machine for the fair. As a good friend, Crono accepts being the guinea pig and allows himself to be moved from place to place. Marle, excited and now feeling safe, decides that she wants a turn and steps up to the machine. Unexpectedly her necklace sets in motion a time travel journey of epic proportions none of them could have expected.