First time I saw an Amiga (first Nebulus on A1000, which was a $2500 computer and therefore out of reach, then Barbarian (Psygnosis) marsh monster with glowing eyes on A500.)
Making bombs in Exile
Discovering the first add-on weapon in Gravity-Force. Suddenly the game opened up.
Walking in those slanted Giger-levels in Turrican and being absorbed by the music.
First hating the intro music and graphics in Datastorm, and then when I got good at it, I flip-flopped! After that I always played through the intro so I could listen to the music before I started playing
First time I completed a level in Virus playing with keyboard.
Landing on the sub in F/A-18 Interceptor. Wow. What a game!
Later, on consoles:
Biked to a friend for a week during Xmas, renting a Nintendo 64 every day just to play Mario World 64! Lava levels with sitar music...
Later, on the PC:
Checking for monsters under the bridge to the silver key in Quake, playing with keyboard only on a 486, and tilting my head to peek, instead of tilting the view. Talk about being "in the game"!
SW:JK, Driver, RtCW.
Being scared awake at mornings by Doom III (try it, was better than coffee!)
The big monster in the roman baths level in HL2.