Off the top of my head...

Final Fantasy VI, although I'm working on that.
Final Fantasy IX, and I'll get to that after VI.
Final Fantasy IV, and someday I'll buy the game so I can actually play it without being a filthy pirate. Maybe.
Final Fantasy III, although now Danielle has it on her DS so maybe I'll get around to it someday.
Ico, I like it when I play it but when I don't play it I don't feel the desire to get back to it. But someday!
Lost Odyssey, which I also intend on finishing eventually.
Crysis and Crysis: Warhead, but I don't know if I'll ever finish those games. I love them while fighting humans but the aliens I just find annoying.
Far Cry 2 - Maybe I'll get back to that someday.
Flower - I will almost undoubtedly finish this someday, as it's not tricky.
HamsterBall - I suck at this game too hard to finish it.
Lara Croft and the Guardian of Light - Danielle and I will probably finish this eventually when we get a hankering for some solid co-op action.
Resistance 3 - Ditto the above.
Ratchet & Clank - A couple of games of this franchise exist on my PSP/PS3 and I might play more of them sometime when I'm bored, but I don't know if this willd definitely happen.