Chrono Trigger was developed and published by Square, and was released in September 1995 for the SNES, and rereleased with Final Fantasy IV as Final Fantasy Chronicles (with some minor unlockable features and some new FMV) for the Playstation on September 29, 2001. The cartridge is fairly expensive (although it's not particularly rare) due to collector demand, but Final Fantasy Chronicles is easily had anywhere video games are sold, and the ROM is readily available and runs perfectly, besides being a bit large. (Chrono Trigger was originally shipped on a 32-megabit cartridge.)
The above info is current as of August 28, 2002.
Chrono Trigger began development in 1993 under the name "The Dream Project," and it certainly had a dream team of RPG designers. Game designers Hironobu Sakaguchi (Final Fantasy) and Yuiji Horii (Dragon Warrior/Dragon Quest) were teamed up with the experienced composer Nobuo Uematsu (Final Fantasy) and relative newcomer Yasunori Mitsuda (later Xenogears and Chrono Cross), as well as the famed character designer Akira Toriyama (Dragon Warrior/Dragon Quest, and a little anime series called "Dragonball"). This combination of the biggest names in the biggest RPG series of all time worked on the game rather quietly, alongside other high-profile projects, until, in 1995, their dream was realized.
Chrono Trigger is the story of a fairly average (if somewhat taciturn) boy named "Crono" who lives in Guardia the year 1000 AD, and opens with him waking up and being seen off to the Milennial Fair by his mother and cat. After meeting up with Marle (who turns out to be a runaway princess) and being sucked into the past (600 AD, specifically) by his inventor friend Lucca's teleportation device...
...well, that would be telling, wouldn't it? Suffice it to say, there's an evil, unstoppable force devouring the world from within, and with the help of Lucca, Marle, a frog-faced knight, an amnesiac robot from the future, an overenthusiastic cavewoman with a limited vocabulary, and maybe a dark mage turned reluctantly to the side of good, Chrono has to prevent the events of 1999 AD, the end of the world.
Yuiji Horii's scenario design talent shows through in the designs of the different time periods. As you hop through time, you'll get to see a depressing post-apocalyptic future of 2300 AD, a just-slightly-different medieval past of 600 AD, an anachronistic prehistory in 65 million BC, and, perhaps most interestingly, the culture most responsible for the events of the past and future, in 12,000 BC, where a magical utopia hovers over primitives trapped in an ice age.
Chrono Trigger, at the time, was stunning for its innovations, as well as the RPG genre conventions that it eschewed. The game lacked a separate screen for battles, as well as lacking standard random encounters. Enemies were plainly visible, and the combat menus would simply come up over the normal isometric view whenever an enemy was touched (or, just as often, an invisible trigger was touched).
Combat itself was also markedly different. While the timing of the combat is the slightly modified turn-based combat of Final Fantasy VI, the special abilities are streamlined, yet elegant. Each character has eight special abilities learned by killing enough enemies for skill points, and skills from different characters combine into Dual (and later Triple) Techs. For example, Lucca's Flame Toss and Crono's Cyclone combine to make Fire Whirl, a version of Crono's Cyclone, only with trailing flames (and extra damage, of course).
Chrono Trigger was also, at the time, a graphical masterpiece. While many of the special effects are no longer particluarly special, the art itself is still impressive, as Akira Toriyama is clearly one of the masters of character design. (The poster art and promotional art, in particular, is quite stunning, and the US cover is probably one of the most memorable box covers for any SNES game.)
It was also one of the most replayable RPGs of all time. If you beat the game by going through the Black Omen, a new mode is opened up: New Game+. In this mode, you retained the levels and equipment from your previous save file, but restarted the game, with an extra portal directly to Lavos. Depending on what point you go into this portal, there are nine different endings (in addition to the three you can get in the normal New Game, for a total of twelve). Between all of these endings and all the side-quests to do, there's a lot of game in this game.
Chrono Trigger is memorable, even today, because of its simplicity and purity. The story is gripping, whether you simply follow the main storyline or wander off into the expository sidequests. The art is amazing, even if the graphics are dated. The musical score puts most movies to shame. The combat is elegant and simple. And all this in a game currently available for a widespread, inexpensive system.
A side note - There was a Super Famicom Satelliview sequel to Chrono Trigger titled Radical Dreamers, notable only in the fact that it tied up many of the loose ends in Chrono Trigger. The plot of Radical Dreamers was reworked (and the game itself was completely redesigned, as Radical Dreamers was a text adventure) into Chrono Cross, which is considered by most to be the true sequel to Chrono Trigger. There is also apparently a third game, rumored to be titled Chrono Break, in development. Little is known about it, as of January 24, 2004, and that name may indeed be a hoax or misunderstanding.
Chrono Trigger || Radical Dreamers || Chrono Cross || Chrono Break(?)
Sources: GameFAQs, Gamers.com, NymNet (http://www.sickduckprod.com/nym/)