My list of co-op games has already been on this list more or less. I'll just go ahead and Echo them anyways.
Borderlands. I played borderlands 2, it's a fun game to co-op, but when we finished I was very much done with it. Has its share of flaws and I tried playing it solo, just couldn't really enjoy it alone.
Monaco. That game was super fun. Very exciting with everybody running around like crazy. Would recommend.
Castle crashes. But of mindless fun, but was still enjoyable. I used to love golden axe style games as a kid, so it was a fun throw back for me.
Diablo 3. This is actually one of my current co-op games. It's been steadily improved from the disaster of its first release. When it first came out I beat Diablo once and was very much done. Now it's like a different (vastly better) game in many ways.
Divinity original sin. This is another fun game. I love the combat and exploring. it's enjoyable with a friend and we're a good bit through on our playthrough. I find it a tad dialogue heavy though, and the writing being sort of lackluster (with a few amusing bits in there), which can lead to me skipping through dialogue and asking my partner what's going on or just not caring.
Not strictly co-op games exactly. But I've been liking the tell-tale style of adventure game (until dawn, wolf among us, etc) to be FANTASTIC "co-op" games with non-gamers. It's mostly story, QTE, and choose what happens. I've found it great to play while non-gamer friend watches like a movie - maybe let them direct the choices. It's kind of an intro to video games disguised as a show or movie and does that role pretty well