Far Cry 3&4 ( coop though with friend though Steam friends )
Althougth Far Cry 3 does have co-op, I can't really recommend it. It's on rails and there's only a handful of missions. If everyone has Far Cry 3 for the great single-player experience, might as well try co-op but I definitely wouldn't recommend this game if the purpose is strictly co-op.
Payday: The Heist and Payday 2. Payday : The Heist is a straight up shooter. Payday 2 has a lot more value though because it has a lot more heists and ways to play. Beware though: Payday 2 is a lot more frustrating than Payday: The Heist especially when trying to stealth. Someone will always blow it and everyone else will be pissed at him/her. If you have someone in your group that doesn't handle losses well, I'd say it is probably better stick to Payday.
Saints Row ( not sure about the 1st 2 )
Saints Row had two-player co-op but the game only released on the Xbox 360.
Saints Row 2, Saints Row 3, and Saints Row 4 all are available on Windows and all also have two-player co-op. Beware that Saints Row 2 doesn't like Windows NT 6 (Vista and newer) and needs a third party hack to slow the game clock down. Despite that, I still think Saints Row 2 was the best.
Torchlight ( upto 3 at least cooperatively, i believe 4 is max )
Torchlight is not co-op, Torchlight 2 is. On Torchlight 2, it supports up to 6 players at once.
I would add:
Monaco: What's Yours Is Mine -- up to 4 players, 2D robbery game
Farming Simulator 2011, 2013, 15 -- up to 8 players (requires ridiculously fast internet) farming game
Kane & Lynch 1 & 2 -- The second one is worth it just for the facepalming. Don't pay much for them though because they're less than 5 hours each.
Space Engineers -- Requires ridiculously fast internet. Build space stations together!
Minecraft -- Build holes in the ground together!
SimCity -- Build a region together!
ORION: Dino Prelue -- Hunt dinosaurs together!
Terraria -- Kill bosses together!
Sanctum 2 (far more so than Sanctum) -- Shoot baddies and defend your base together!
Test Drive Unlimited 2 -- Cruise together!
Sins of a Solar Empire -- Gang up on unsuspecting AI together!
Supreme Commander (1 & 2) -- See above!
Freelancer -- A classic!
Ace of Spades -- Shoot the enemy, or each other!
Alien Swarm -- Free to play! Survive alien hordes together and for the love of gaming try not to shoot each other!
Borderlands 1 & 2 -- Not at the top of my list but qualifies.
Call of Juarez: The Cartel -- This is a lot like Kane & Lynch in that it is short but it is still a good 3 player co-op game.
Command & Conquer 4: Tiberian Twilight -- Okay, seriously, the only reason why you'd want to play this is to see how far C&C has fallen.
Demigod -- Like DOTA but with less humans and more AI.
EYE: Divine Cybermancy -- A strange game but co-op able.
Fable III -- Two players can make a baby. Need I say more?
Firefall -- Free to play. Just please don't get sucked into its MMOness.
Guns of Icarus Online -- Haven't played this one much to be honest but it is designed to be co-op (a time of 4 versus other teams).
Orcs Must Die 2 -- See post above mine.
Plants vs Zombies: Garden Warfare -- You are a plant and with 3 other plants, you must prevent zombies from eating your garden. 'Nuff said.
Darkspore -- Up to four us's against thems.
That's about all I see worth mentioning in my Steam/Origin library. I obviously excluded the RTS games that have multiplayer that can be played cooperatively.
I also didn't hit on the really old titles like SimCity 2000 Network Edition.