My favorite RPG has to be Chrono Cross. The game has a fantastically deep plot coupled with a very amazing soundtrack. Though don't expect to catch the plot on a single playthrough. You're gonna have to do some searching on the internet to truly comprehend the sheer magnitude of Cross's story. The "prequel" Chrono Trigger is very good, too.
As far as Final Fantasys go, my favorite was IX. Great characters combined with a great, uplifting story, and great sidequests (Chocobo Hot & Cold is just the best minigame/quest ever) make this a very enjoyable game. V was also good, as was VI, VII, and XII for me.
SRPGs are also among my favorite games. The Disgaea series is one the best examples of a great SRPG. Mind boggling depth in its gameplay and a light hearted story (the 1st has a better story by far while the 2nd's gameplay is easily better). Of course, as some already know based on chat hijacks, I really enjoy the Fire Emblem series. Finally, Tactics Ogre: Let us Cling Together is also one of the best SRPGs I've ever played and, quite frankly, one of the best games I've ever played. Its only English release was for the PSX, though good luck finding it for under $80. Its still a great game to play, even if you have to play it in Japanese on an SNES emulator. There's a great fansite floating around the interweb that does a bang-up job of translating the fantastic story and options.
Lastly, "action" RPGs like the Tales series are also a lot of fun to play. Most of the time, the story is only passable but the gameplay is just so much fun. Tales of Symphonia and Tales of the Abyss are two great RPGs one should look into (although it's a shame EUers can't play Abyss). The older PSX games (Tales of Destiny, Destiny II, Eternia) are also interesting games, but imo are harder to get into and enjoy than ToS and ToTA . The Star Ocean series is also good (although SO3 sucks for every moment you're not in battle). Hell, anything Tri-Ace makes is great.