Hm. Hard to say, really. There were quite a few of those special moments for me. I think I'm going to let the Diablo series take three of them, though. This list is in no particular order, but I do think the first one takes the cake as the "best gaming moment."
1. The fight with the Butcher in Diablo.
Yeah, it's been said many times already (pointed out earlier), but this really was one of the most intense and memorable scenes of any video game ever made. With the chilling tale the dying nameless man had to tell you, and the confrontation with this formidable monster in his room full of blood and corpses. Many of my heroes fell, but the sorcerer eventually reigned supreme.
2. Becoming a Grandmaster Swordsman in Ultima Online.
I played this game for years with my mom and my brothers. It was my first MMORPG, and the only one I can say I still really like. Reaching the maximum skill level for Swordsmanship made me feel so awesome.
3. Defeating the "ubers" and identifying my first Hellfire Torch in Diablo II.
I actually played Diablo II on and off for years before finally deciding that multiplayer was more interesting than going solo. I've met so many people here, and I've made long-lasting friendships with some of them, thanks to this game. When I first saw what the Hellfire Torch was, I knew I had to get one for myself, and I had set out to collect keys with my friends, using my poorly-equipped paladin (specialized in Zeal)... One of my friends had a very well-geared smiter and offered to kill the ubers for me at no cost. Together we killed all of them, and I picked up my very first torch. It was an 18/20 Paladin Torch... and another "friend" stole it from me only days after.
4. Killing the Cyberdemon and discovering the location of Hell in The Ultimate Doom.
The epic showdown between the space marine and the biggest demon on Deimos. My weapon of choice being the Rocket Launcher, of course. Looking back, I find it difficult to believe I ever had trouble killing this guy. He's slow, dumb, and has an attack pattern that you will learn within seconds. Just after a couple minutes of strafing and firing out fifty rockets to his face, he's done for... and the scene after is unforgettable... "Deimos floats above Hell itself!"
(Almost let the ending to Final Fantasy IV take 4's place, but I just couldn't.)
5. The release of Diablo III.
I've been a big fan of the series for as long as I can remember. There were always rumors going about in D2... about what D3 would be like, and if one would ever be made. I had always hoped for a D3, myself, and I'm glad to see it's finally here. On release night, I sat in TeamSpeak with my friends, and we all rapidly attempted to sign on at midnight. After what felt like several hours, we were finally able to get in a game together, to journey off and destroy Diablo once again. I got my money's worth with this game. It sucks to see so much hatred for it on its own official message board, but you can't please everyone. Remember, D2 wasn't perfect when it came out, either. No game is, I think. Either way, May 15th is a night (or morning) I won't forget.
I know, enough about Diablo, but literally half of my life was THIS GAME. Thank you, Blizzard.