Borderlands 2 still my favourite co-op.
Left 4 Dead is great too, although it's 4-players. Bots are kinda annoying and removing them for 2 players isn't really an option (difficult to do and game becomes brutally unfair for beginners).
Played a lot of Torchlight 2 co-op as well. It's a Diablo 3 clone, so might as well go with the original (which i liked better).
Portal and Portal 2 have a co-op mode.
Dying light has co-op too. Good game.
Trine 2 also? Never really tried.
Serious Sam(s) are a blast, co-op. Not sure how it plays online, mostly played LAN. The last one was OK, still required beefy internet on server.
And of course, Minecraft.
Most games are RPG, so 2 hours sessions will get you to progress, but will take a while to complete.
L4D2, a campaign can take a leisurely 1 hour, and the content is relatively small (about 8, 10 campaigns, some harder than others).