My absolute favorite computer game, of all-time, is the original Civilization. I played the HELL out of that game when it was out. The various sequels have all been fun, and great, but they don't have the fond memories and nostalgic feeling to them that the original game does. There wasn't a free moment spent alone that wasn't on Civilization back in the day.
Although Star Wars: Empire at War is coming very close to breaking into an all-time favorite.
We're the middle children of history...no purpose or place. We have no Great War, no Great Depression. Our great war, our defining crucible, is a spiritual war.
I was also a big fan of the Wolfenstein, Doom, Quake, and Sim City games. I also have fond memories of King's Quest III and many more fond memories of Space Quest IV. And I'd be remiss not to mention Oregon Trail (which I managed to put on my PSP, woohoo!) and Odell Lake.
However, for some reason, this thread makes me long for the days of local BBSes and their door games. You know, those text-based classics whose graphics were, at their best, ANSI or RIP. My all-time favorite was probably Trade Wars 2002, followed closely by the original Legend of the Red Dragon and Hack 'n Slash. Incidentally, you can still find some BBSes out there that are accessible by telnet, but for some reason it just doesn't seem the same.