Hearthstone - free

Diablo 3: Reaper of Souls

Path of Exile - free

L4D2

Dragon's Crown

Dynasty Warriors 8

Resident Evil 6

Sonic & All Stars Racing Transformed

Divinity: Original Sin.

Super Smah Bros. Melee on Gamecube. #Yesallsystems.

Hearthstone!!!!!

Wow, that's a monstrously huge question! Lemme throw out a few less known or unusual ones: Dungeon Siege III, Beyond: Two Souls, Dead Space: Extraction, Double Dragon Neon, Lara Croft and the Guardian of Light, Cloudberry Kingdom, Ninendo Land. Okay, some of those are well known but they're all very fun!

Left 4 Dead is an amazing game if you're playing co-op with friends.  Other than that I don't know what else I can add here.  HAlo is fun too, co-op.  Me and my bro used to always play that.  

Catherine and Portal 2 for PS3 and Tetris Attack for the SNES. Gotta rep for the co-op/comp puzzle games. 

Dragon's Crown is probably the best beat-em-up I've played since Konami's licensed brawlers from the early 90s. Up to 4 players, online or offline.

The Simpsons Arcade game is also on PSN and XBLA, for that matter.

Anarchy Reigns (PS3/360), from Platinum Games.

Team Fortress 2. Besides that, I would also like to try the co-op of Risk of Rain.

Some of my favorites include:

Super Mario Kart (SNES) others in the series are good, too

Smash Bros. series

Nintendo Land

Wii Sports

We Ski & Snowboard

Soul Callbur series

Protect Me Knight (indie Xbox LIVE game)

Castle Crashers

BattleBlock Theater

The Legend of Zelda: Four Swords Adventures

Kirby Air Ride

That should hold you for a while.

My oldest son & I love playing the Gears of War games together.  My kids love playing the Lego games.  I also enjoy playing Final Fight, Sengoku 3, 8 Man, Cyber-Lip, Double Dragon, Battle Toads, and other arcade beat'em ups with my kids too.  

There are a lot of games on XBLA & PSN that are worth your time, but they're not cheap.  I make a list of games I hear are good and wait for the sale.  I own over 50 games from XBLA & PSN and probably paid full price for less than 10 of them. 

My favorite recent co-op games are:

Castle Crashers
Portal 2
Lara Croft and the Guardian of Light
Splinter Cell Conviction
New Super Mario Bros. Wii 

I have only one(series) Littlebig Planet 1, 2, and Karting

Played a lot of Crackdown, Borderlands 1 and 2, Gears of War series, and now Earth Defense Force 2025. Not to mention the hoards of FPS games I've played co-op like the Halo series and COD before Modern Warfare. I often use the co-optimus web site to find new co-op games to play. It's my favorite game mode period.