Orcs Must Die 2.

Shoot Many Robots. Dungeon Defenders. Saints Row the Third.

Saints Row the Third

diablo III

well Farcry 3 its fps but insane.
or go with something like vegas 2 even tho its older its great 3PS

Torchlight 2

tl2 even though i didnt play it that much

Not all released in 2012, but here are a few multiplayer games that my friends and I enjoy.

Trine 2 - Nice semi-puzzle game for lan/online co-op play. Switch between three heroes (magician/knight/thief) with unique abilities and enjoy the funny storyline.

Torchlight II - Not really to my liking, but a friend of mine is on it all the time. Top-down hack and slash with a focus on getting awesome loot.

Dota2/League of Legends/Awesomenauts/MOBA-style games - Either you love them or you don't.

Orcs Must Die 2 - Great two-player game. Trying to find ways to make traps compliment each other while being able to take down both the low-health but speedy goblin things and the strong and tanky trolls can be challenging, but watching those orcs die feels good.

Dungeon Defenders - Amazing game with elements of both tower defense and FPS. If you don't like FPS while she does, one of you can plant towers while the other goes FPS. Or both go towers. Or both FPS. It's up to you! Can get slightly grindy at later levels, though. Nightmare mode is a bitch.

Jamestown - Co-op top-down bullet hell shooter (like touhou games), with different levels of difficulty and an old school gauntlet mode (2 lives, complete all levels). Great if you only have time for a short 10~15 minute game session.

Portal 2 - With the steam workshop out, there are quite a few good quality community-made co-op puzzle maps. Great if you two love Portal.

Guild Wars 2 - My girlfriend and I love it, so I'm just going to put it in here. Casual players might miss out on the legendary weapons, but the lack of a monthly fee lets you come back and enjoy it at your own pace.

not really from 2012 but worth a look are: Dead Rising 2 + DR2:OTR,Sacred2,Titan Quest and Orcs must Die 2.Also Saints Row 3 for random goof's (and youre done goofed)

Of the ones i played i would say it is a tossup between Orcs Must Die 2 and Borderlands 2, both are very fun games.

borderlands 2

Borderlands 2 ofc

Rayman Origins. I played 4 player co-op on the 360 and it was one hell of an experience, I haven't laughed that hard with a co-op game since SSB Melee. If you can set it up to play it local co-op on PC I highly recommend it.

Black Ops 2 Zonbies.

Saints Row : The Third if you want to play it with your Girlfriend! ^^

Orcs must die 2 and portal 2 are amazing co-ops xD

Borderlands 2

Syndicate, but it's an FPS. Dark Souls is cool too but can be challenging at times.

Borderlands 2 by a long shot. If you want a game to play with your girlfriend, I'd suggest Dungeon Defenders. A friend of mine and his girlfriend seem to enjoy it. Note: I've never tried it myself. I'd suggest tonnes of FPS coop games, but as you're not much into them, it's kind of pointless.

I liked Castle Crushers. They are very fun to play.

Natural Selection 2

Torchlight II

Borderlands 2.

borderlands 2

Well, what do you like?

I really like Orcs Must Die! 2, but that has TPS components to it. E: ah, you got OMD2, nice :>

Others that were released this year:

Critter Crunch (arcade puzzler, has a versus mode and a co-op survival mode)
Magic 2013 (definitely recommend this if you both like strategy/tactic games)
Wanderlust: Rebirth (awesome 8bit co-op action adventure game)
Awesomenauts (technically a MP game, but you can play cooperative bot matches--it's a sidescroller moba)
Torchlight II (very popular action RPG)