I came to this thread expecting to give a fairly short list, but it got a little longer reading the other posts. Anyway,
Zelda: OoT - Couple of times on N64, Master Quest on GCN.
Prince of Persia: Sands of Time - Awesome ending.
GTA San Andreas - Once on PS2, once on PC. Sunk a ton of time into on the PC, but still haven’t ever completed it.
Halo - Different difficulties, Co-op and solo. I've probably played each level on legendary several times, but not in order.
Jet Grind Radio
THPS (N64) - My memory card kept deleting the save... I probably completed it five times (Every skater, everything).
THPS3 - GCN and Xbox
Eternal Darkness - 3 times, for the "Uber Ending."
Rush 2049 - Played thoroughly on N64 and DC. Never completed (haven't ever found all the hidden medals/whatevers).
REZ - It's an hour long... of course I've beaten dozens of times.
Ratchet and Clank: Up your Arsenal - Probably twice.
Ratchet: Deadlocked - At least 3 times
Guitar Hero II - "Beaten" on Expert on PS2 and 360.
Resident Evil REmake - Claire and Chris (does that count?).
Donkey Kong Country - Who knows?
Tetris Attack (Story Mode) - Several times, probably only once on the secret extra hard difficulty.
2D Marios - Who didn't?
No One Lives Forever 2 (PC)
I'm sure there are other old ones I'm forgetting, but that's a pretty good list considering I don't usually consider myself as someone that replays games.