Time travel's been a part of sci-fi ever since the genre started. Sometimes it's integrated well into a story, sometimes not. It really had never been present in RPGs before 1995. Enter Chrono Trigger, Square's "art-house" project, just a year after the successful Final Fantasy III. Featuring the company's best designers, it was hyped in Nintendo Power like mad, and it became one of its most lasting successes.
Chrono Trigger does so many things well it's amazing. It features its share of RPG cliches, of course (in the beginning, mostly), but it uses them so well that you can't really bitch about it, especially since there are plenty of original turns. The central idea, of course, is time travel - there are five distinct eras that you can travel between (plus one for the final boss and one for your "base" of sorts), and what you do in the past really does affect the present and future. It's kind of hard to describe, but you really will be surprised by some of the changes, and more by how well everything is fitted together - one time travel will take you somewhere, then after you do something in that era and go someplace else you'll find another portal to a third era, and eventually wind up where you started, after a couple of dungeons and maybe a new ally or two. It's one of those things that'll make you go "Oh. That was clever, how they did that."
The game is on the surface brighter and more cartoony than Final Fantasy III (the characters are crude anime drawings done by Akira Toriyama, known for his hack art in DragonBallZ), but occasionally it can reveal a much more brooding, morose side. You'll first see it in the future (2,300 A.D.), a bleak wasteland populated by a few ragged, starving humans, but the game doesn't really fully unfold until after an epic battle between humans and dinosaurs in the prehistoric era, when you'll go through a nondescript gate to 12,000 B.C. If you haven't played the game yet, do try to get to this point without spoiling it for yourself - the scenes that ensue are some of the most memorable in RPG history (as in "Whoa! Dude..."). The game's centerpiece is the things you'll do in 12,000 B.C., when the entire plot finally becomes clear. And after watching all that, some other scenes, like the end of the creature in the Keeper's Dome in the future, become unexpectedly moving once you find out the whole backstory. And when the game takes a lighter tone (rarely out of place), it actually succeeds in being humorous (as opposed to many games that try to be funny and end up being retarded).
The overall coolness is enhanced by the graphics, the pinnacle of the Super Nintendo's capabilities, and the soundtrack, composed by the two Square greats Uematsu (Final Fantasy) and Mitsuda. The latter found his first big break in Chrono Trigger and later moved on to compose for Chrono Cross and Xenogears. (Let me re-emphasize that: Chrono Trigger's music is good. Given the hardware limitations, what Uematsu and Mitsuda have done here is really amazing. It's one of the only three game soundtracks that I would recommend owning separately on CD.) Mood is always set very well by the lighting and the music (which sometimes gives way to eerie drips, moans, and wind effects). And the battle system, though similar to Final Fantasy's, introduces a fine twist in the form of combined attacks (e.g. if Crono has Cyclone and Lucca has Flame Toss, they can combine to do Fire Whirl), later adopted by games like Suikoden. And to top it all off, it featured the brilliant New Game+ option - once you beat the game, you can start over, but with the same pumped-up, end-game-level fighters that you had in your first save file, so if you just want to blow through it for the story, you easily can. (This idea was also used later in games like Vagrant Story.)
Chrono Trigger still fetches a high price on Ebay. Hell, the very fact that Square has decided to remake it for the Playstation (as half of Final Fantasy Chronicles) speaks for itself. It's one of the few games that don't fade into obscurity when their system becomes obsolete. Square, having courted greatness since 1989, concluded its SNES days powerfully with Chrono Trigger - it was a fine precursor to the company's future enormous success on the Playstation.