Beat em up: Tekken 3 (PS)

Fighting: Super Smash Brothers (N64)

Platform: Super Mario Bros. (NES)

FPS: Goldeneye (N64)

TPS: Dead Space 2 (X360)

Sport: Soccer (NES)

Stealth: Never really played any stealth games.

Survival: Infection mode in Perfect Dark Zero (X360)

Adventure: The Legend of Zelda (NES)

Role-playing: Final Fantasy: Crystal Chronicles (GC)  Edit: Actually, Pokémon Blue (GB) was long before it.

Sandbox: Grand Theft Auto III (PS2)

Strategy: Settlers III (PC)

Simulation: The Sims (PS2)

My brain memory modules are pretty rusty...let me try to recall some titles...

Beat'em'up: Karateka (ZX Spectrum)

Fighting: The Way of the Exploding Fist (ZX Spectrum)

Platform: Donkey Kong (Arcade)

FPS: Wolfenstein 3D (PC) (well, Battlezone (Arcade) actually, or Tau Ceti (ZX Spectrum), but I think those are more arcade sims than FPS)

TPS: Cabal (C64)

Sport: some soccer game on ZX Spectrum (can't remember which one)

Stealth: not sure what I played first, Beyond Castle Wolfenstein (C64), Infitrator (ZX Spectrum) or Saboteur (ZX Spectrum)

Survival: Project Firestart (C64)

Action-Adventure (back then known as arcade-adventure): Knight Lore (ZX Spectrum)

Role-playing: Dungeon Master (Amiga)

Sandbox: Elite (ZX Spectrum) (or Miami Vice (C64), really hard (and kinda bad) game which I always saw as one of precursors to GTA)

Strategy: Blitzkrieg (C64)

Simulation: Tomahawk (ZX Spectrum) (or Battlezone (Arcade) if we count that as tank sim)

Racing: Pole Position (Arcade)

Adventure: The Hobbit (C64)

Shoot'em'up: Scramble (Arcade)

Beat em up:  Battle Arena Toshinden (PS1)

Platform: Jumping Flash! (PS1)

FPS: Timesplitters 2 (PS2)

TPS: Syphon Filter (PS1)

Sport: PGA Tour 96 (PS1)

Stealth: Metal Gear Solid (PS1)

Survival: Resident Evil: Code Veronica X (PS2)

Adventure: Tomb Raider 2 (PS1)

Role-playing: Final Fantasy VII (PS1)

Sandbox: Grand Theft Auto 3 (PS2)

Strategy: Command & Conquer (PS1)

Simulation: Theme Park (PS1)

Racing: Ridge Racer (PS1)

I managed to dodge three of these genres completely until last generation it would seem, impressive.  It was only last generation that I discovered the world outside of Sony, too.  By the time I was discovering the wonders of the Gamecube, it appears I had played every genre!

Beat em up: no idea
Fighting: either a soul calibur or a street fighter of some sort
Platform: Super mario world (SNES)
FPS: Medal of Honor (PS1)
TPS: Vanquish (PS3)
Sport: FIFA 99 (PS1)
Stealth: Metal Gear Solid (PS1)
Survival: Honestly I think Zombies in Black ops (PS3)
Adventure: Uncharted: Drake's fortune (PS3)
Role-playing: Dragon Age: Origins (PS3)
Sandbox: Grand Theft Auto Liberty City Stories (PSP)
Strategy: Tropico 3 (PC)
Simulation: Theme Park (PS1)

FPS: The Catacomb Abyss 3D
Adventure: Indiana Jones and the Fate of Atlantis
Action Adventure: Little Big Adventure
Action: Star Wars: Rebel Assault
Sport: NHL Hockey or FIFA International Soccer (not sure)
Strategy (RT): Dune II: The Battle for Arrakis
Strategy (TB): Sid Meier's Civilization
Simulation (economic): SimCity 2000 or The Settlers (not sure)
Simulation (flight): Comanche: Maximum Overkill
Simulation (space): Wing Commander. Privateer
Simulation (managerial): Anstoß
Racing: Car and Driver
RPG: Lands of Lore: The Throne of Chaos or Betrayal at Krondor (not sure)
Platform: Commander Keen 4: Secret of the Oracle

All on mighty MS-DOS

Project FIrestart was bloody amazing stuff and probably the first 'real' survival horror (but I"m sticking with Haunted House ;)

Yeah, played the shit out of it back in a day, really amazing game, true predecessor to survival horrors as we know them. Funny thing is game was influenced heavily by Alien movies, ship's name was Prometheus and years later we have Prometheus (as Alien prequel).

beat em up: Tekken 

Fighting: Battle Toshindin - I think thats the name

Platform: pandemonium

FPS: Quake

TPS: Bloodrayne? PS2

Sport: Jonah Lomu Rugby

Survival: cant remember

Adventure: cant remember

Role-playing: Pokemon Blue

Sandbox: cant remember

Strategy: Age Of Empires

Beat em up: TMNT (Arcade)

Fighting: Karate Champ (Arcade)

Platform: Donkey Kong (Arcade)

FPS: Wolfenstien (PC)

TPS: Jet Force Gemini or Burning Rangers? (N64 or Saturn)

Sport: Winter Olympics (Gameboy)

Stealth: Thief II (PC)

Survival: Resident Evil (Sega Saturn)

Adventure: Legend of Zelda (NES)

Role-playing: Phantasy Star IV Genesis)

Sandbox: GTA Vice City ( Didn't like it and still don't like the genre. (PC)

Strategy: C&C (PC)

Simulation: MS Flight Simulator (PC)