I am going to preface this by saying, if you have never played Chrono Trigger, go to an emulator site right fucking now, download it, play it, and then come back. This is possibly my most favorite game on the face of the planet (other than Monkey Island, World of Warcraft, and Grim Fandango), and it was ultimately what got me into the genre of the RPG as a video game.
One of the key principles of this game, which I thought was really neat (other than the Active-Time Battle System, which was also used in Final Fantasy Games), is the idea of time travel. Players are able to play across 7 eras in the game world, meeting new party members, and fighting battles that would be otherwise unavailable. What's especially cool is that the actions the player takes in the past effect the outcome of the future. There are 13 unique endings, which I think is extremely forward and well thought out for a Super Nintendo Game.
My favorite eras of time to play in were either the prehistoric era, where humans and dinosaurs coexist; or the post-apocalyptic one where robots and humans roam side-by-side. The two party members that you pick up from these two eras are Prometheus, a robot who's fixed up by Chrono's trusty mechanic friend Lucca, and Ayla, the fearless leader of a tribe who constantly fights against a group of walking reptiles known as the reptites. Maybe I just liked Ayla because of her tiny fur bikini (I've always loved playing sexy characters), or maybe I liked her for her rage, fury, and incoherent sentences; either way, she's a badass.
Basically, the whole story starts out with Crono, Lucca, and Marle (a princess in disguise), and Lucca attempting to show the two how her time travel machine works. Unfortunately, something goes awry, and Marle disappears right before the duo's eyes. They meet up with frog, in order to try to find Marle and get her back, but end up in back in the prehistoric ages in order to fix Frog's sword. The whole story, after that, gets a bit complex, and is constantly changing as one shifts back and forth between eras. Thus, I'm going to suggest that you play it on your own to get a bit of a feel for it, rather than have me describe the whole story to you bit by bit.
Later, a sequel to Chrono Trigger came out for Playstation 2 called Chrono Cross, which was equally interesting, but will never have such a strong place in my heart as my original, favorite RPG did. What can I say? Nostalgia owns this electric heart.
GO BUY IT!