Oregon Trail was crack for 3rd graders back in my day. The days we got to go to "The Computer Lab" to play that was like Christmas.
And Karateka on Atari was the bane of my existence as a kid. Those fights where the guys had birds to help them? Freaking impossible.
The oldest game I have that I'm still working on (and by that I mean I will probably never get around to beating it) is "Alice." It's only from 2000, so it's not all *that* old, but I got soooo far on it before and then my hard drive died. I've heard the ending is worth beating it, so I've never given up hope!