Top contenders are:
Assassin's Cree Brotherhood - Seven nominationsCall of Duty: Black Ops - Six nominations
Heavy Rain - Six nomination
Mass Effect 2 - Five nominations
LIMBO - Four nominations
Super Mario Galaxy 2 - Four nominations
Full nominations list...
Action
Assassin's Creed: Brotherhood (Ubisoft Montreal)Battlefield: Bad Company 2 (Electronic Arts/DICE)
BioShock 2 (2K Games/2K Marin)
Call of Duty: Black Ops (Activision Blizzard/Treyarch)
God of War III (SCE Santa Monica Studio)
Halo: Reach (Microsoft Games Studios/Bungie)
Artistic Achievement
Assassin's Creed Brotherhood
Call of Duty: Black Ops
God of War III
Heavy Rain (Quantic Dream)LIMBO (Playdead Games)
Mass Effect 2 (Electronic Arts/BioWare)
Best Game
Assassin's Creed Brotherhood
FIFA 11 (Electronic Arts/ Electronic Arts Canada)Heavy Rain
LIMBO
Mass Effect 2
Super Mario Galaxy 2 (Nintendo)Family
Dance Central (Harmonix)Kinect Adventures (Microsoft Games Studios/Good Science Studio)
Kinect Sports (Rare)
Kinectimals (Frontier Developments Ltd)
LEGO Harry Potter: Years 1-4 (TT Games)
Toy Story 3 (Disney Interactive Studios/Avalanche Software)
Gameplay
Assassin's Creed Brotherhood
God of War III
Heavy Rain
LIMBO
Mass Effect 2
Super Mario Galaxy 2
(What no Angry Birds?)
Handheld
Cut the Rope (Chillingo/Zeptolab)Handheld
God of War: Ghost of Sparta (Ready at Dawn, SCE Santa Monica)
LEGO Harry Potter: Years 1-4
Professor Layton and the Lost Future (Nintendo/Level 5 Games)Sonic Colours (SEGA/Sonic Team)
Super Scribblenauts (Warner Bros Interactive Entertainment/5th Cell)
Multiplayer
Assassin's Creed Brotherhood
Battlefield: Bad Company 2
Call of Duty: Black Ops
Halo: Reach
Need for Speed: Hot Pursuit
Starcraft II: Wings of Liberty
Original Music
Alan Wake (Remedy)Fable III (Lionhead Studios)
Heavy Rain
James Bond 007: Bloodstone (Bizarre Creations)Mass Effect 2
Super Mario Galaxy 2
Social Network Game
Bejeweled Blitz (Popcap Games)Farmerama (Bigpoint)
FIFA Superstars (EA Sports/Playfish)
My Empire (Playfish)
Zoo Mumba (Bigpoint)
Zuma Blitz (PopCap Games)
Sports
F1 2010 (Codemasters Birmingham)FIFA 11
Football Manager 2011 (SEGA/Sports Interactive)Gran Turismo 5 (Polyphony Digital Inc)
International Cricket 2010 (Codemasters/Trickstar Games)
Pro Evolution Soccer 2011 (Konami/Winning Eleven Productions)
Story
Alan Wake
BioShock 2
Call of Duty: Black Ops
Fallout: New Vegas (Bethesda Softworks/Obsidian Entertainment)Heavy Rain
Mass Effect 2
Strategy
Civilization V (2K Games/Firaxis)Fallout: New Vegas
FIFA Manager 11 (EA Sports/Bright Future)Napoleon Total War (SEGA/Creative Assembly)
Plants vs. Zombies XBLA (PopCap Games)
Starcraft II: Wings of Liberty (Blizzard Entertainment)
Technical Innovation
Assassin's Creed Brotherhood
Call of Duty: Black Ops
Halo: Reach
Heavy Rain
Kinectimals
Super Mario Galaxy 2
Use of Audio
Alan Wake
Assassin's Creed Brotherhood
Battlefield: Bad Company: 2
Call of Duty: Black Ops
DJ Hero 2 (FreeStyleGames)LIMBO
BAFTA Ones to Watch Award in association with Dare to Be Digital
Mush (Angry Mango)Sculpty (Team Tickle)
Twang (That Game Studio)
GAME Award of 2010
(vote here)Call of Duty: Black Ops
Dance Central
FIFA 11
Halo: Reach
Heavy Rain
LIMBO
Mass Effect 2
Need for Speed: Hot Pursuit
Red Dead Redemption
Super Mario Galaxy 2