Chrono Trigger

1995 saw the release of a game created by a dream team consisting, among others, of such artists as Hironobu Sakaguchi—the creator of Final Fantasy—Akira Toriyama—the creator of Dragonball—and renowned composer Nobuo Uematsu. It was based on the standard RPG format of the time, but featured several innovations including a lack of random battles, over a dozen possible endings, and extensive, character-building sidequests. Graphics that were lovely for the time remained the same for the Playstation reissue (2001 in North America) but several anime sequences were added, regardless. Fun gameplay, an interesting plot with multiple variants, and the option to recruit a villain as a playable character are just some of the reasons that Chrono Trigger is consistently judged one of the best games of all time.

When Crono bumped into a girl at the Millenial Fair, he certainly didn't expect to end up travelling through time in an effort to stop a global catastrophe. Still, when Marle—the girl in question—vanishes into a strange portal while trying out a prototype teleportation device invented by Crono's friend Lucca, he doesn't hesitate to step in after her. It's the first step in a trip through human history, a massive war of humans versus the Mystics, and the gradual awareness of a parasitic creature that will destroy civilization if Crono and his friends can't stop it.

Images:

The good guys, of all shapes and eras
The Mystics
The showdown with Magus
The ultimate enemy is... a hedgehog?
Opening movie for the PSX

The Legend of Zelda: A Link to the Past

This third incarnation of Zelda is arguably the best. In 1991 (1992 for North America), A Link to the Past took the original formula, added several new elements, shook them up, and presented the world with a dazzling snowglobe of adventure. The inclusion of a more detailed story, the invention of such staples as the Master Sword and the hookshot (quite possibly the coolest item in the history of gaming), and the establishment of a dual-world that has been included in nearly every Zelda game since all go into making this game exciting, memorable, and, most importantly, fun.

Young Link is at home one rainy night when he hears the telepathic voice of Princess Zelda calling for help. His uncle heads out to rescue her, but Link, following behind, soon finds his injured uncle and takes over his mission. The wizard Agahnim is trying to break the seal on the Dark World, where Ganon is imprisoned, using the descendants of the sages who created the seal in the first place. The Master Sword is the only weapon capable of stopping him, and so Link sets out on his multi-part adventure to find the sword, stop Agahnim, save Hyrule, and, as always, save Zelda.

Images:

Smuggling the pricess to safety
A full inventory is a happy inventory
The Light World
The Dark World
Opening movie

Final Fantasy VI

1994 saw the release of the last Final Fantasy game for the SNES, although, as with IV, it was misnumbered in the North American release as III. Featuring an intricate story, fully-fleshed characters, the largest playable cast of any numbered FF game to date, the introduction of steampunk to the series, and one of the most memorably evil villains, it's another contender for the best Final Fantasy game.

Terra Branford has grown up as a slave under the control of Emperor Gestahl. Locke Cole is a "treasure hunter" with strong anti-Empire leanings. When Terra breaks free of imperial control and is found by Locke, a chain of events is set in motion that will break apart the world as it is known. Joined by Celes, a general of the Empire who realizes what's going on; Edgar, king of the neighboring country of Figaro; his brother Sabin, an ascetic; Shadow, an assassin with a secret; Cyan, a man who has lost everything to the predations of the Empire; and a small host of others, they try to stop Gestahl and his insane right-hand Kefka from exploiting the Espers—a race of magical people—and conquering the world.

Images:

Icons of the entire playable cast, in order:
Terra, Locke, Edgar, Sabin, Celes, Shadow, Cyan, Mog, Gau, Setzer, Relm, Strago, Umaro, and Gogo
Concept art of Kefka
The self-proclaimed Angel of Death
Intro sequence for the PSX
Opening scenes on the GBA

Final Fantasy IV

Although fourth in the series, this 1991 offering for the SNES was only the second to be released in North America, and is often still referred to as Final Fantasy II for that reason. It has, like the original game, been remade several times for a number of systems. As the innovator of any number of conventions that would later be used in the series and notable for having the first playable Cid—a character that has appeared in some form in every FF since II—this game is among the top contenders for the highly contested rank of Best Final Fantasy Game Ever.

The story focuses on Cecil, Dark Knight and captain of the Red Wings, the fleet of airships belonging to the country of Baron. After being sent to a peaceful town to steal a Crystal in what amounted to a massacre, Cecil questions his king's motives. Given a vague reassurance, he is sent on a mission to deliver a package to another town. Accompanied by his best friend, Kain—who can't quite disguise his love for Cecil's girlfriend, Rosa—Cecil journeys to Mist, home of the Summoners, only to discover that the package he is carrying is actually a bomb. The entire town is obliterated, leaving a young girl as the sole survivor. The girl, Rydia, summons Titan with the last of her strength, causing an earthquake that changes the landscape and separates Cecil and Kain. Angered by the betrayal and grieved by the destruction he inadvertently caused, Cecil undertakes a quest to redeem himself and stop his former king. Betrayal, redemption, and sacrifice abound as Cecil gathers companions only to lose them again, culminating in an otherworldly showdown with a force of primal hatred and destruction.

Images:

Concept art of Cecil
Concept art of Kain
Concept art of Rosa
Concept art of Cecil, post-redemption
Screenshot of Cecil confronting Baron's king
Cecil and Kain fighting the Mist dragon
Game introduction video for the GBA vs. the SNES
Trailer for the DS remake