Well for me it was definately beating Civilization 2 when I was a kid. (PS1 version - without cheats, I don't remember the difficulty, if this version even had any to choose, but I guess it was normal)
As for the greatest, I think it was Stalker SoC... the extreme redux mod, on the highest difficulty. It was a great achievment, advancing from a poor rookie with a jacket to a full fledged veteran. I became a sort of a godlike stalker(thats normal in vanilla, but redux... it was difficult). I wasn't invulnerable in any way, but the skills that I had developed, the equipment I've gotten and everything else that comes with it... wow I wish it was an mmo just to show people my character.
I'd like to point out my most bitter vicotry as well. Me and my friend were playing Diablo I on the playstation (yeah it was a long long time ago). Well we came to the beggining of the 14th level without saving. But thhe problem was that the memory card wasn't in the playstation, and I figured, hell I'll just tuck it in adn save. But alas it didn't work. He glanced at me, a tear in his eye, we knew what we had to do... REPEAT THE WHOLE ONE DAY GAMING SESSION AGAIN!
BTW this is my first post here, glad that I finally registered. Looking forward to spending some time within this great community.