Co-Op Games which are fun to play with non-gamer-GF

Rapelay

The Adventures of Shuggy.

portal 2, saints row 3-4 and dead space 3 <3

I played Mount your friends and Payday 2 with my girlfriend. She seemed to enjoy the mounting more than the shooting though.
you could try that out.

guacamelee, jamestown and magicka could be fun

crash team racing

if she isn't a gamer and doesn't know what genres she likes i would play the folowing games on my desktop with her:

• dynasty warriors (easy to learn but with a lot of deapth especially when you reach harder stages and dificulties. its grindy nature makes it easy for beginners)
• Lego (easy to play, choose a franchise she likes)
• CIV or other hex turn based games (normally these games on easier dificulty setting are incredebly easy but still give the ilusion of weekness
• sports game (for example if she likes football/soccer, then fifa is a great way to pass the time. with only a 6 buttons needed it's easy to learn and even if she doesn't play well you can "carry" the team if you play on low dificulties)

Those are the co-op games i recommend for people that never played anything, however i think the best approach to make someone start playing video games is actually leting them play a singleplayer game with you encouraging and guiding. My GF liked magic, binding of isaac, football manager and unholy heights before she played (almost) everything with me. The sessions we played on those games, at first, were me coaching and explaining basic gamy stuff like red barrels blow, AI "needs" to cheat to keep up the human mind, the game says quickly move here but if there's no timer then there's no rush,etc.

Just because nobody mentioned it yet, I'll say "Monaco". Perfect for local co-op with two controllers at the same machine and great fun.

Mortal Kombat.

Trine 1-2 .. Castle Crashers .. Lara Croft and The Guardians of Light .. Awesomenauts .. make your pick

Counter Strike, against bots. You will be her hero.

Download the free Gang Beasts and play that

Portal 2. Best online purchase I've ever made.

BattleBlock Theater

DOTA 2

Dark Souls Prepare to Die Edition

I played many COOP games with my non-gamer gf. :)
Try Sonic Allstars Racing Transformed, it's like Mario Kart.. my girlfriend loved it.

As some members already said... Rayman legends is the best, artistic, great gameplay, fun.
Other great co.op GF games are Trine 1 & 2, Battleblock Theather, Kart games (like SOnic all star), Lara croft guardian of light, Little big planet for the PS3 and last but not least, Child of Light (take the smaller role and teach the mechanics, its great and poetic :D)

Depending on her taste in TV series, also The Walking Dead and The Wolf Among Us.
Not exactly "multiplayer", but still great to play/watch together. :)

Just be carefull not to end up fighting over the game - Lara Croft and the GOL was pretty good at creating discussions here :P