Does the contra a good game that you can think of when it comes owning the old games. I am sure it does fall into the category of old games. And even the house of dead was one that I owned in that time.
The oldest game I own is probably Mortal Kombat X. I've been buying newer games ever since the Xbox One came out. So that was right after the start. Or tbh I have Thief from a previous games with gold free release that's also one of the first games to release for the X1. The oldest game I play though is Skyrim which I have a remastered version for on Xbox One that even has cheats you can unlock so that makes it quite interesting.
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.