Hm, what a beatiful question. Heres my list:
NES - Battletoads, hands down the best platformer. Zelda without map nor english knowledge was a nightmare. And as a russian, we did not have the original NES everyone else had. We had dendy, a horrible chinese clne, with fked up games. Maybe @Adult Cat Would recall.
SEGA - Comix Zone, just love this game.
PS1 - Gran Turizmo amazed me back then. Gta 3 was the 1st gta i ever played.
PC - 1st pc game i ever played was diablo2. God how many hours me and my friends wasted playing d2 on battle.net. Then came Scape.