Chrono Tigger
Chrono Trigger, is a time traveling game done properly! Crono, Marle and Lucca (all from 1000 AD) get transported to another time and find out their world is going to be destroyed by something called Lavos. With no idea what it is or really how to stop it, these three take their chances and hop times. They met new friend and enemies, they change time. Traveling to prehistoric ages to post apocolytic futures - this group of friends have a lot to do if they want to stop Lavos. Since, this is all about time travel and saving the world, what else will they be able to save? Also what will they lose at the cost of time travel?
Chrono Cross
Chrono Cross, the next part but without time travel and taking place about 16 years after. The story follows a teenage boy name Serge. One day he is meeting his friend, Leena, at the beach next thing he knows he is being called a ghost and some girl named Kid wants him to help her. Kid wants something called the Frozen Flame because it grants wishes. Serge and Kid find that Kid's mission is tied to a whole lot of messed up and Serge's past. With dragons, magic, fairies and demi-humans, the world is about to be in trouble again. Turns out, parallel worlds all because of something that happened to Serge as a child.
Quick Notes
And no, you don't have to play one in order to understand the other. I'm fond of both Chrono Trigger and Chrono Cross but I know others who will only go one way. Both are available on the PSN.