The oldest game I can recall offhand that I still own is M.U.L.E. for the Atari 800. Still have the 5 1/4' floppy disk that the game came on too. The game was released in 1983, six years before I was born.
Also have a bunch of old DOS games from the mid/late 80's. Sopwith being one that comes to mind. Still have the original Leisure Suit Larry series, King's Quest and Space Quest lying around my house somewhere, I still have yet to go dig through all the mounds of old floppy disks.