I think it was because I had very few geeky friends while growing up that I never got into the whole pen-and-paper RPG thing. Instead, I marveled at the worlds created inside the computer. Even today, one of the things I look forward to most with games is exploring a new character-development system in a strange new world, hoping that I won't see the limits to it anytime soon (most recently expreienced in Oblivion). Again, it's very hard to classify games in this genre, mostly because almost all games I like contains RPG elements (whatever that may be), but here goes:

Role playing games
Fallout 1 & 2 (PC)
Final Fantasy Tactics Advance (GBA)
Pool of Radiance (C64)
Ultima IV: Quest of the Avatar (C64)

Runner-ups
Deus Ex (PC)
Diablo (PC)
Ultima V (Amiga)
Ultima VII (PC)
Planescape Torment (PC)
Pokémon Gold (GBA)