Games with a Puzzle touch are usually preferred, although we'd take a look at pretty much everything.
Just as long as it's coop, and not pvp, or such.
Some coop games I play with friends or I have heard good things about
Warhammer: Vermintide (Plays almost exactly like Left 4 dead but with a focus on melee combat, 4 players)
Portal 2 (has a coop campaign)
Borderlands 2/presequel (I liked 2 more, but its up to 4 player coop FPS/Diabloish game)
Helldivers (A madcap top down shooter where you have to complete objectives with your teammates. Part of the appeal is that things can get kind of crazy, and while there is no PvP, friendly fire is turned off, and you are expected to die by your teammates or from yourself a lot, be it being caught by friendly fire, getting in the bullet path of your own turrets, or blowing yourself up with a grenade amongst other tragically fatal but hilarious deaths)
Risk of rain (2d sprite based beatemup of sorts, has online coop and a generally frantic, frenzied pace as the difficulty gets higher the longer you play. A+ soundtrack)
Castle Crashers (Arcade style beat em up)
The only real puzzle game is portal 2 amongst those, however.