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 the ability to travel through time, which the plot uses a lot.

Story
Crono, the main character, wakes up one day ready to go to the once-in-a-lifetime Millennial Fair and have fun. His childhood friend, Lucca, has decided to build and show off a teleportation machine for the fair. While on his way to see her invention, Crono bumps into another girl, Marle, who decides to accompany him. As a good friend, Crono volunteers to be Lucca's guinea pig, allowing 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. As Lucca and her father work the controls, Marle's necklace begins to glow, setting in motion a time travel journey of epic proportions none of them could have expected.