Favourite Genres:
Platformers
First Person Shooters
Character Action (Hack & Slash)
Playstation:
Strider 2
Tony Hawk's Pro Skater 2
PS2:
Burnout 3: Takedown
Devil May Cry 3
Ratchet and Clank: Up Your Arsenal
SSX: Tricky
SSX On Tour
PS3:
Bayonetta
Killzone 2
Metal Gear Rising
Ratchet and Clank Future: Crack in Time
Resistance 3
Rock Band Blitz
PS4:
The Last of Us
Transformers Devastation
Xbox:
BLACK
NHL 2004
Unreal Championship 2
Xbox 360:
Alan Wake
Gears of War 2
Lost Planet: Extreme Condition
SNES:
Super Turrican
U.N Squadron
Nintendo 64:
Goldeneye
Sin and Punishment
Super Smash Bros
Gamecube (Favourite console of all time):
007: Everything or Nothing
Bloody Roar: Primal Fury
F-Zero GX
Metroid Prime 2: Echoes
Sonic Adventure 2: Battle
Super Mario Sunshine
Super Smash Bros. Melee
Wii:
Madworld
Super Smash Bros Brawl
Genesis:
E SWAT
Sonic 2
Sonic 3
Sonic & Knuckles
Vectorman
Saturn:
Dreamcast:
Game Boy Advance:
Kirby: Nightmare in Dreamland
Mech Platoon
Sonic Advance 2
DS:
Animal Crossing Wild World
Infinite Space
Ninja Gaiden: Dragon Sword
3DS:
PSP:
Burnout Legends
Resistance Retribution
Rock Band Unplugged
WipEout Pure
PSVita:
Killzone Mercenary
Persona 4 Golden
Tearaway
Arcade:
Marvel vs. Capcom 2
New Zealand Story
Time Crisis 2, 3 and 4
PC:
Battlefront 2
Bastion
Cave Story +
Civilization 5
Counter Strike
Counter Strike: Global Offensive
Final DOOM
Killing Floor
Half Life
Half Life: Opposing Force
Marlow Briggs and the Mask of Death
Most Played Game: Super Smash Bros. Melee
Best (2) Game(s) of All Time: Bayonetta and Tony Hawks Pro Skater 2
But seriously, it's hard to pick just two.
EDIT: Fixed list with Travis's improvements so it doesn't take the entire screen.