Listing these as chronologically as possible. Most aren't really related to one single part in a game, moreso just the experiences they've offered...
-Playing Super Mario Bros. on the NES,
-beating Shredder and Krang in TMNT II,
-beating Sonic 2,
-seeing Mortal Kombat for the first time
-beating Super Mario RPG,
-playing Chrono Trigger for the first time,
-playing FFIII (SNES) for the first time,
-controlling Mario in 3D in Mario 64, jaw dropped over visuals,
-playing NiGHTS for the first time,
-bought my PlayStation with FFVII,
-opening of FFVII & ending,
-Resident Evil 2; being scared shitless,
-playing the first GTA,
-Metal Gear Solid - all of it,
-getting Zelda: OoT Gold Cart for Christmas / playing it,
-opening of FFVIII & ending,
-opening of Lunar: Silver Star Story,
-playing Silent Hill for the first time,
-Mario Party with friends
-opening of Chrono Cross / amazing music,
-playing a demo of Sonic Adventure prior to the DC's launch,
-Dreamcast launch + hype (hope),
-PS2 launch + hype,
-Metal Gear Solid 2 E3 trailer / demo / playing it,
-Silent Hill 2 E3 trailer / playing it all of it & ending,
-death of the Dreamcast
-realizing how open-ended GTA3 was,
-experiencing ICO,
-playing a demo of Rogue Squadron II prior to the GCN's launch,
-GCN launch + hype,
-Super Smash Bros. Melee with friends,
-opening of FFX & ending,
-Xbox launch + hype,
-having Halo LAN parites with friends,
-experiencing REZ,
-Zelda: Wind Waker's graphical change / playing it,
-Halo 2 midnight launch,
-Metal Gear Solid 3 E3 trailer / playing it, crying at the ending,
-realizing how bat-shit insanely open-ended GTA San Andreas was,
-playing Resident Evil 4 for the first time,
-360 launch + hype
-playing Gears of War / jaw dropped over visuals,
-PS3 launch + hype,
-Wii launch + hype,
-playing Zelda: Twilight Princess for the first time,
that's all I can remember, phew!