Do remakes of old games count? If they do, I've got the Origins version of the original Final Fantasy. Original was released in 1987 on the NES, Origins was released in 2003 on the PS1.
I wasn't born in time to get hold of anything older than the 32-bits, so other than remakes my oldest game is Robo Pit, released in 1996 on the PS1. But I plan to fix that soon.
[small]Robo Pit is a surprisingly good game, though.[/small]