It is impossible for me to pick only one RPG as my all-time favourite.
Ultima VII: The Black Gate (PC) features what may still be the best-realized fantasy world. The main storyline wasn't anything special, but the detailed world, "living" NPCs, portrayal of a society in decay, companions that played more of a role than just extra swords... There are good reasons why this game is still highly regarded and projects like Exult exist.
Fallout & Fallout 2 (PC) - I don't think I need to elaborate much on these. Fallout was the original and had a more consistent atmosphere, but I think that Fallout 2 was a more fun game to play. Other than the Temple of Trials, which is one of the most tedious intro segments in any game.
Knights of the Old Republic (Xbox) is a rarity in that it's a Star Wars game that I actually like. I've been a huge fan of the movies since the first one was in theatres, I love the prequel films and Return of the Jedi too, I hate the novels almost without exception, and I've found most of the games to be uninspired (other than X-Wing, TIE Fighter, Jedi Knight). KOTOR is an absolutely brilliant game, and I think it finds a very good balance between nonlinear gameplay and strong storytelling. You do have to complete all four middle worlds eventually, but you can do them in any order and don't even have to complete one before moving on to the others. There are many optional sidequests, and many events in the game play out very differently, depending on your choices. It's not as open-ended as Fallout, but being too sandboxy wouldn't really feel true to the source material. Presentation values are top-notch, and I was astounded with the amount and quality of voice acting in the game. The characters and storyline were great, and I may actually like KOTOR even more than Fallout, as blasphemous as that may sound.
Chrono Trigger (SNES) is better than any of the Final Fantasy games, as far as I am concerned. The characters are memorable, the story is interesting and sends you to a variety of "worlds." It was 1994-95 and they had already dispensed with the random battles. The story is fairly linear, but unlike most JRPGs, your choices do have a dramatic effect on the outcome of the story. The game has 17 documented endings, some of which are obviously more simliar to each other than others. It's one of the only games that I know of where you can finish the game without the main character. One of the first games to feature "New Game+" that allows you to start the game with your characters' stats and items intact, and doing so opens up an ending halfway through game that you wouldn't have been able to accomplish the first time through. Square has yet to top this one.
Skies of Arcadia Legends (Gamecube) does have a lot of fantasy cliches, but it's damn fun and uplifting. The characters are generally optimistic and cheerful, driven by a simple love for exploration, and it's a nice departure from the angst-ridden navel-gazing of brooding, sarcastic anti-heroes that seems to have become popular. Just when you think you've explored the whole world, new regions open up, there are tons of hidden discoveries to find, ship-to-ship combat, recruting crew members, and a cool element-based combat system. It's from the team that did Phantasy Star II and IV.
Planescape: Torment (PC) needs little explanation as well. Brilliant concept, mostly-brilliant execution, fantastic art direction. Only thing that really holds the game back is, ironically, the AD&D rules that the Planescape license is stuck with.
Deus Ex (PC) is one of those hybrid or cross-genre games, but it's still a damn brilliant game. It has its share of flaws (like goofy AI), but it's got a fantastic story and doesn't force the player into a specific way of playing the game. Has just enough RPG stats to serve the purpose of the game (unfortunately dropped from the sequel), and is deservedly one of my all-time favourites.
Okami (PS2) will ruffle some feathers by being on my list, but it's an action-RPG by any definition I've seen. Playing as a goddess incarnated as a wolf is unique, and the game throws an incredible variety of environments and challenges at you. The artistic direction is flat-out amazing, like a living Japanese watercolour painting. You learn "celestial brush" techinques (which can be upgraded) to paint solutions to puzzles into existence (or for use in combat) and to restore life to the world. It's an incredibly rewarding experience to watch the dead and blasted landscape burst to life as the direct result of your actions.
I would also include Legend of Zelda: Twilight Princess and Ocarina of Time, but I'll definitely get the "Zelda is an adventure game and not an RPG" crowd all riled up, despite their RPGish elements and the influences they've had on the RPG genre.