The three that stand out most to me are: Suikoden 1 & 2, Final Fantasy Tactics, and Deus Ex.
The best way to explain Suikoden 1/2 would be to imagine if Mass Effect 1/2 were 2D PSX RPGs. They're set in ye olde ye RPG land with medieval technology, but the narration and characters and story were absolutely top-notch. If you love SNES-style RPGs and/or story, play Suikoden 1 and 2.
Final Fantasy Tactics is a strategy RPG that will seem odd at first, but if you can stick with it you will find a story that's rife with betrayal, manipulation, kidnapping, murder, treachery, corruption, and vengeance. Oh, and no romance allowed.
Deus Ex. Everytime it's mentioned, somebody will reinstall it. Deus Ex is set in the year 2052 where a dystopian world is teeming with government/corporate corruption and conspiracies. The developers' stance on the story is "If it's in the game, someone, somewhere believes it." You start in America, but end up traveling to many locations throughout the world.
While technically an FPS, there are a lot of RPG elements in play, such as using your character's skills to hack computer networks, pick locks, and disable alarms. Even talking to friendly NPCs can sometimes give valuable information (such as security codes) that will help you complete your objectives. If you like sci-fi stories and/or hilariously bad [http://www.youtube.com/watch?v=NG1qKzIsisU] voice acting [http://www.youtube.com/watch?v=5DAPXMZk2iw], you need to play this.