Sonic-
Being from Europe we were more exposed to Sega than Nintendo and when I first saw the Mega Drive version of Sonic after having played the Master System version to death I was totally gobsmacked at how much superior it was technically.
Street Fighter-
To me as a kid SF was just the coolest game with uber cool moves and characters.
Virtua Fighter-
This was the first time I experianced incredibly fluid 'life like' animation in 3D so that blew me away.
Mortal Kombat-
Again as a kid I thought the gore, digitised sprites, music and characters were just awesome.
Donkey Kong-
The game that made me ask myself- "Surely the SNES cannot possibly be capable of producing such astonishing graphics and sound!"
Streets of Rage-
I think you can see a trend developing here. Anything with cool characters with cool special moves bashing up others just looked amazing in my eyes. I loved side scrolling beat em ups and I can thank SoR for that.
Super Mario World-
Possibly the best platforming game I have ever played to this day.
Super Mario Kart-
The most multiplayer fun I've ever had. Ever.
Sega Rally-
I remember me and a childhood friend having dozens of hours of fun racing each other with slower car boost turned on.
NiGHTS Into Dreams-
The first time I got used to controlling Nights was amazing.The most dreamy like game I've ever played with an A Life system yet to be bettered.
Super Mario 64-
3D platforming had arrived....and yet to be bettered. What a magical game.
Legend of Zelda: Ocarina of Time-
Perhaps my favourite game of all time.
Grandia 2-
Didn't play JRPGs before and this game showed me what I've been missing. Loved everything about it.
Shenmue-
Wow what an amazing technical accomplishment I loved living in Ryo's world and throwing myself into his quest to avenge his father.
Halo-
Never was into FPS too much but Halo showed me that all I had to do was get used to the controls and then soak myself into a wicked Sci Fi universe and fight like a super soldier.
I haven't bothered with anything this gen as it's still ongoing but special mention must go out to Half Life, Mass Effect and Uncharted.