Strategy: Final Fantasy Tactics
RPG: Earthbound (Mother 2)
MMO: Asheron's Call
I think I've played through FFT at least 6 times now. I play it a lot more now as I fly cross country once or twice a year and I always end up busting it out for PSP on the plane; once I start I just can't stop till I beat it again.
Honorable mentions (game or franchise in no particular order):
Metal Gear Solid
Final Fantasy 5, 6, & 7
Little Big Planet
Grand Theft Auto
Secret of Mana
This is more like a list of drugs that I can't quit than favorite games.
WoW (Proudmoore): Scy - Undead Rogue
FF14 (Behemoth): Zaya Xuaro - Fish
TOR: Scy Fang - Sith Tanksassin, retired
GW2 (YB): Scy Fang - Thief, retired