Well, Pokémon games with their corresponding remakes would be a safe answer. Other than that, I happen to own a copy of Ghostbusters: The Video Game, Rango, and TMNT for three different consoles since they play differently. I'd also say Kingdom Hearts: Chain of Memories and Shadow of the Colossus: for the former I own the original GBA game and two copies of the PS2 remake, and for the latter I own two copies of the PS2 version, black label and greatest hits, and the PS3 HD version.
I guess Metal Gear Solid: The Legacy Collection would apply here, too.