Oh fine, I'll do this too.
BEST FUCKING GAME SERIOUSLY: Saint's Row IV
BEST GAME THAT'S NOT AN OVERGLORIFIED DLC PATCH: Starbound
BEST DEMO: Metal Gear Rising: Revengeance
BEST NON-GAME GAME: Rocksmith 2014
BEST NON-2013 GAME PLAYED IN 2013: Metal Gear Solid 3: Snake Eater
BEST NON-2013 GAME PLAYED IN 2013 FOR THE FIRST TIME: Demon's Souls
HONORABLE MENTIONS
Saint's Row II, for being what would eventually become Saint's Row IV.
Dust: An Elysian Tail and Bastion, examples of what a modern 2D game can actually look like.
Gravity Rush, for making me feel slightly better about buying a Vita. Slightly.
NintendoLand, for making me feel slightly better about buying a Wii U. For about an hour.
Exquisite Knorpse 3, for not being sold off to Gearbox and released unfinished.
And Ys: The Oath in Felghana, for being Oath in Felghana.