Hi guys. I'm looking for some coop games to play with my girlfriend. She likes good stories, so I guess I should be more after RPGs, but other genres should also work. Can you recommend me some good coop games? Possibly some not weighting 20GBs or so, and with "standard" requirements. :)
EDIT: I have WoW as a possibility, since it is a great game for beginners. Also, Dungeon Siege 2 is a small possibility, anyone coop-ed it?

How about Madballs in Babo:Invasion ?

As for Dungeon Siege 2 (and pretty much any Diablo-clone): Pretty much made for co-op, piss-poor story.
That being said, I have never gotten past the desert in Dungeon Siege 2 (the second "area" you visit :p), but the only diablo-clone that really grabbed me was Torchlight.

It looks nice, but too bad it doesn't have any sort of multiplayer.

Trine is good. Though I'm not sure how coop works there.
And if you are okay with Diablo clones, you should probably try Sacred too.

I just played Din's Curse co-op for the first time a few days ago. Suffice to say, it is one of the most hilarious games I've played co-op in. Besides being a fairly solid ARPG, it's gameplay mechanics are interesting and unpredictable, resulting in many lulz-worthy deaths. No good story in there though, but you get to "make" your own story if that's your thing.
Also, if you're thinking of WOW, maybe you can consider AoC. I haven't played that in a long while, but I hear the expansion is fairly good. Besides, AoC's lore is built on the existing Conan/Hyboria mythology already established 85 years ago, and the quests are very well written too.

Titan Quest can be quite fun coop, much better then dungeon siege 2 as well.

Do you have two gamepads? If yes:
LEGO Star Wars (preferably the complete saga, you want either that or 1 + 2, not all three)
LEGO Indiana Jones
LEGO Batman
LEGO Harry Potter
They're all available for most recent consoles and PC, though the handheld versions lack coop (afaik).

No gamepads. Two laptops connected via a switch, so its either LAN or split-screen.
EDIT: Arcade games with split-screen option are cool too. :)

Let's think outside the box: have you heard of "Sleep is Death"? It might be interesting for you.
http://sleepisdeath.net/

Serious Sam has legendary co-op. Although it is slim on story, this is replaced by "the story" of the shared experience with a lot of "Holy Sh*t" moments. It's a simple, adrenaline fueled primal experience.
Serious Sam is one of the few co-op based games that my wife will play. I think this has a lot to do with the approachability of it and the fact that it's consequence free with infinite respawns in co-op mode.

Try Icewind Dale 2. It doesn't have as much of a story as the Baldur's gate series, but it's pretty much built around co-op multiplayer. It isn't overly complicated, but could take a bit to learn the various rules and spells.

Oh, forgot.
NWN2: Storm of Zehir actually IS co-op friendly (I think). So worth a look.

Borderlands