Tetris. I have bought more copies of Tetris than I know what to do with. Every phone either my wife or I has ever owned (even when we were dating. I used to buy the game and give her money for it because my phones battery lasted like three seconds.) NES, Gameboy... actually, screw listing all this. It's a lot, probably 20 copies or so over my life in some iteration.

I've got 3 copies of FFVII and FFVIII. 2 Hardcopy PSX versions, 1 PSN each. My neighbor scratched up my disc 1 for VIII so I bought a new copy, FFVII was a minor freakout induced by my father. I was in middle school and looking at his records, and he told me how he had to buy an extra copy of Darkside of the Moon because he played the first so much it wore out. I then became convinced I was going to wear out FFVII when i was 30 and never be able to find another copy to play it again.

FF Tactics x2 (PSX, War of the Lions)
FF X 3 (NES, PSP, Origins set)
FFVI x 2 (Anthology, PS3)
FFV x 2 (Anthology, PS3)
FFIX x 2 (PSX, PS3)
Comix Zone x3 (Genesis, PSP Genesis comp, and PS3)
Costume Quest (360, PS3. Bought it for Xbox, forgot that I bought it for Xbox because I never play the bugger, rebought it for PS3)

I'm sure there are a boat load of others, mostly retro games that I have copies of in Atari collections or Genesis compilations etc.