2 x Sonic Gems Collection: I bought it for the Gamecube originally because I assumed that like almost every other Gamecube game it would have a 60Hz mode. It didn't. I then bought it for the PS2 fairly recently because it's easier to play with the Dual Shock controller, because I had a lot more space on my PS2 memory cards and because I could rip both Sonic CD's soundtracks from the PS2 version to my computer.
2 x Orange Box: Bought it for PC originally then bought it for the PS3 because I find it easier to play that way.
2 x Sega Mega Drive/Genesis Collection: One for the PS2 (which ended up being superseded by Ultimate Collection on the PS3) and one of the PSP, just because I like some of those games so much that I'd want to play them on a portable.
2 x Final Fantasy VII, VIII and IX: Spares in case any of them ever break.
2 x Final Fantasy IV: One came as part of Final Fantasy Anthology European Edition and one came as part of Final Fantasy Chronicles.
3 x Resident Evil 4: Originally got it for the Gamecube then was appalled by the graphical quality when I upgraded to an HDTV. Got the Wii version after that because I thought it would be a lot better graphically (it wasn't) and finally on the PS2 because I heard that the PS2 having a higher colour depth (24 bit as opposed to 16 bit for GC/Wii) made the game look a bit better. PS2 is probably the best looking one to play on an HDTV, IMO.
3 x Theme Park: PC, PSX and DS, because I love it that much.
2 x Theme Park World (Sim Theme Park): Originally got it for the PC but the PC I had at the time couldn't run it very well so I bought the PSX version.
2 x Grand Theft Auto Liberty City Stories and Vice City Stories: Originally bought them on the PS2 when I didn't think I was going to get a PSP, then got them on the PSP when I did.
2 x Grandia II: Originally for PS2, saw the PC version extremely cheap and bought it more out of curiosity than a plan to play through the game on the PC.
2 x Curse Of Monkey Island: Bought it originally back in the 90s and then recently when I saw that they were re-releasing a bunch of LucasArts point-and-click games as budget titles I bought it again.
2 x Resident Evil 2: PSX original and Gamecube port, I mainly play the Gamecube version now (slightly better graphics) and have the PSX as a spare.
2 x Wind Waker: Got the first version for Christmas one year, then a couple of years later I found a brand new first edition (containing the bonus disc with OoT/Mater Quest on it) and couldn't pass it up.
2 x Super Mario All-Stars: SNES original plus Wii version, because I love the game and my SNES is basically dead.
2 x Advance Wars Dark Conflict/Days Of Ruin: So that my partner and I could play it together and also because I was curious to see how different the translation was between the European and American versions.
2 x Professor Layton and Pandora's/The Diabolical Box: When Curious Village was released in Australia, Nintendo Australia used the American ROM and artwork as the basis of the Australian version, but from the second game onwards they switched to the European version, including Luke's utterly horrible European voice using a different actor. Had I known this at the time I would have just imported the American version straight away.
I tried not to include ports that differed too much from the original game (like the original Super Mario 64 and Super Mario 64 DS or Persona 3 and P3P), games that have the same name but are completely different on each console (like Civilization Revolution on the PS3 and the DS) or games that both me and my partner had bought separately before we met.
...Shit, didn't realise I had so many.
