When I first finished Gods - of course. A very special moment.
When I finished Planescape: Torment, a game that was so good I never really wanted it to finish. When I finally completed it, I felt as if a chapter in my life was reluctantly closing, because that game really gets to you.
(I felt something similar when I completed Thief II, but not as profoundly).
When I completed Crisis Zone at the arcades - I knocked over the office level and the bomb level with only one health bar remaining - it was literally nerve fraying stuff! It was also cool because a small crowd had gathered behind me to see if I could finish the game, which I did.