Judicat0r: Space Invaders (Atari 2600).
.
You
beat Space Invaders? I honestly didn't even know that was possible. Beside, many of the games of that era, even if actually possessing a final level, are so difficult to beat that literally only a handful of people on earth have ever done it.
"Oldest Game You Own You've Beaten" You specify 'game', and not 'video game' or 'computer game'.....so golf? Or solitaire?
Alright, alright! Before thinking about it in depth, King's Quest (1983) is the oldest game I've beaten (And I only needed one hint, for the "riddle" that everyone knows is inexcusable!).
I've been trying to beat Scott Adams' Adventureland (1978) since I was a kid. I refuse to resort to hints, but I haven't give up yet. I just started my first playthrough of Zork (1980), so if I ever complete it, that would elbow out King's Quest, unless I remember an even older game that I have completed.