Vagrant Story
The World Ends With You
Parasite Eve

I'm terrible at *completing* RPGs, so I'll add to the list games I've spent a considerable amount of time on and plan to beat (so as to flesh out my list, because I'm a dirty cheater)

Chrono Trigger: I chipped away at it from time to time in High School, but I got burned out by the end game, started a new game and having a lot more fun with it

Valkyrie Profile: I LOVE this game, and would've beaten it already if the game allowed me to play Disc 2 (the PS1 US version suffers from a defective print that causes even the tiniest scratch on the disc to render the game unplayable). From what I did play, it's arguably one of my favorite RPGs, and I look forward to the day I can play the whole thing (I hate emulation, and I lack a PSP, but I might cave in to one of those options).

Super Mario RPG: No real excuse here, other than my Wii's at my parents' house 2 states away.

I also plan on beating at least one story in SaGa Frontier, but that game is VERY opaque.