Pokémon Gold/Silver (GBC, 2000)
I didn't think anything could surpass Red/Blue/Yellow and then this came along. I was living in Atlanta when it came out but the buildup was amazing. They had display Gameboy Colors in Target and Walmart and I spent so much time on them. The series introduced some important features that still hold true today: new regions, separation of Special into Special Attack and Special Defence, day and night, breeding, but most importantly, 100 new Pokémon. It has since been remade for the DS and will be re-released via the Nintendo 3DS Virtual Console on 22nd September.
Championship Manager 01/02 (PC, 2001)
I can't for the life of me get into Football Manager. 01/02 holds my heart. I play with updates from the real world as not to feel too archaic and it's the last great game before the change. It's thin on the ground for realistic features but thanks to some special patches, it's not so bad. Playing it vanilla and you get some legendary players who couldn't imitate their "digital" careers.
Super Mario World (SNES, 1990)
One of my favourite early childhood memories (see F-Zero and Sonic 2 below). I was lucky enough to play it on a Virgin Atlantic flight and it was the best thing in the world. Riding Yoshi was like nothing I had ever done before.
F-Zero (SNES, 1990)
Another fond childhood game. I only ever played this at my friend's house as he had a SNES and I wasn't allowed one. It's easily my favourite driving game. Incredible soundtrack, super addictive gameplay and then-state of the art graphics.
Sonic 2 (Sega Genesis, 1992)
Christmas 1993. My cousins got this for their Sega Genesis. I got to play it and enjoyed every moment. I got to know Sonic before Mario (who I've played more of in my lifetime). It's an instant classic and includes good old Myles Prower.
Honorable mentions: Mario Tennis (N64), Pokémon Puzzle League (N64), Tetris (GB), Ronaldo V Football (GBC), System Shock 2 (PC), Kingdom Under Fire: A War of Heroes (PC), Super RC Pro-Am (GB)