There are a lot, but here are a few. Reading some of the above reminded me of a few of these.
-Stepping out in Seyda Neen after being granted my freedom at the beginning of Morrowind. I had no idea what to do, so I just started walking. I kept walking for three months.
-Emulating Pokemon: Blue on my computer one Christmas break. We had huge blizzards so we were pretty much snowed in for four weeks. I heard about this game on the news of all places and was instantly hooked.
-Playing various n64 games at friend's houses (I never had one). The first time I played Mario 64 I was absolutely blown away by the 3D world that we got to explore. That was topped, though, by the time I showed up at a birthday party to discover four friends playing this new game called Goldeneye. That was the best birthday party I've ever been too.
-I've had a lot of good COD4 games, but one recently was especially satisfying. I had been playing with two friends on Team Deathmatch for awhile, and we kept getting absolutely murdered by this other group. The current game was Bog, which is a favorite of mine because I'm a pretty decent sniper. I was doing well but the rest of my team was still getting killed. We were down by nine kills and the other team only needed one more kill to win the match. And then I got a chopper. I called it in and started yelling at my team to hang back. Bog is a very open map and my chopper started reeking havoc. I saw one of our guys was about to get shot so I yelled at my friend to flash the enemy player, and as he did my other friend shot him. It took about twenty seconds for my chopper to get the winning kill. I've never had a win feel that good.
-This one sticks in my mind the most, but is hard to explain. I was playing Giants: Citizen Kabuto as one of the space marine guys. I was winning pretty handily when I came over the top of a hill. Down below me in the valley were bunch of burrowers and some tank things. And they all saw me. As I stifled an "oh shit!" I quickly backed up over the hill. It was too late though, and as I began to run two furious mounds of dirt appeared over the crest of the hill on both sides, flanking two huge fireballs fired down the middle. I was toast.