The first arcade game I ever saw - Pac-Man - in a Godfather's Pizza in Colorado Springs, was astonishing. I'd seen and played Pong before that, but this was actual images, not dots (well, technically). It was crazy.
Zelda. The first game I ever played where it wasn't obvious what to do. The freedom was mind-blowing. That game made video games into a lifelong hobby for me. Before that, they were just interesting diversions.
Street Fighter II. The complexity of the move sets was a revelation. It was a total addiction for me, for months, and even longer once I had an SNES.
The first time I saw Wolfenstein 3D running on a friend's PC. That's what convinced me I needed a PC of my own (just in time for Doom). I'd never seen such fast, fluid 3D. Before Wolfenstein, 3D was a choppy, rather gimmicky concept.
The pack-in Playstation launch demo disc. Specifically, the one-lap Wipeout demo. Another high watermark in fluid 3D.
Mario 64 - nope. I adore the game. But the real "OMG" N64 moment was a bit later: the release of Wave Race 64. REAL WATER in a game. Not just pretty water, but real, physical, interactive water with waves that can make or break your lap time. I still maintain that it really hasn't been topped in that regard.
Soul Calibur on Dreamcast - it wasn't the game (it's just Soul Blade 2) nor the graphics that wowed me. It was the motion capture, specifically the characters' weapons demonstrations, and the lip-syncing in whatever options menu that was that let you make them say phrases.
The Metal Gear Solid 2 demo disc that came with Devil May Cry was amazing. Just walking around and looking at the water puddles, reflections, and hiding in lockers and such was more memorable than the final game turned out to be, for me.
Booting up the Gamecube for the first time. It was my first imported console, and showing it off to a friend before it was in stores (we played Monkey Ball all night) was a real treat.
Metroid Prime. Pretty much all of it, but especially those immersive moments - rain on the visor, Samus' reflection during a blast.
My first time at E3, seeing and playing Twilight Princess after that hours-long wait.
I could go on. There are so many.