I think the oldest game I've got is Major Stryker, which is a PC game that was released in 1993, and which I've had since...'94? I was a little kid at any rate. I played that game so many times, I memorized where nearly every enemy spawned, so for a challenge, I used to play by only tapping the "shoot" key in time with the music. :P
Oldest non-PC game...well, actually I've got some NES cartridges, but I never played them (my mom got them and the system free somewhere, but I think it was missing something...can't remember for sure, but we couldn't get it to work), so I don't really count those. So I suppose it'd be Final Fantasy 7.