Not sure if you mean in chronological order of release or just the game I've had for the longest time. Both are hard for me to answer.
Right now the oldest game I got is probably the Atari 2600 game's "Combat" which seems to be from 1977. That is the oldest one I have right now and one of the earliest game I ever played, although it is not the same copy.
I had to move overseas so I practically went on a quest to rebuy consoles and games I left behind, so if you are asking what game copy I have stuck with the longest that is harder for me to answer, it'd have to be a copy I brought from Mexico. I think that'd be my Link's Awakening cartridge. I don't even know if it still works but it is one of my few possessions I could bring with me.