Alpha Centauri, Civ type game by Sid Meier. Never played it though. In RL Alpha Centauri is one of the closest stars to own own sun.
My favorite game that I actually completed has to Thief:The Dark Project. And went on to replay it many times. I would love to say Thief II:The Metal Age, but I didn't get into it as much. Favorite game that i haven't completed is GTA IV.