First one that came to mind:
Opening up the last door in Wolf3D to see the final boss there with dual chainguns waiting to tear me up
Others that I thought of after reading this thread:
The day my first 3D accelorator arrived (16MB STB Velocity 4400, a TNT1 card (that wasn't neutered like the later models were)) and loading up the sIn demo in full 3d glory.
Playing JediKnight online (first game), up until this point, I was still using the keyboard to play fps's. No mouse. I beat the whole game like that I think, it's hard for me to even comprehend that now. Also was my first (and last) clan experience, I got booted because I had to go on a business trip to San Jose (which I notified the clan about ahead of time) for a week and couldn't make one practice.
JK introduced me to a lot of new stuff as a gamer. Circle strafing (before I played using the arrow keys, left/right were to turn), the mouse, and online play. I had this Supra modem with a led readout of my connection speed that I'd use so I could gauge how badly I'd lag.
I had a pretty memorable moment last fall playing RtCW. After watching the cutscene for the level where you're in the catacombs, I was seriously afraid to jump into the hole and start my trek. I didn't want to die at the hands of the undead
