How about Castle Crashers? Its a crazy 2D cartoony slasher with coop for up to 4 people, with some light RPG elements in it (you upgrade a few stats, character's special ability, collect new gear).

There are also some additional modes like arena and volleyball.

It's quite fun.

Another vote for Portal 2 and Orcs Must Die 2, the former in particular.

EDIT: And if you're into sandbox rampages, the Saints Row games are good. Saints Row 2 is my favourite, but the PC port is atrocious; SR3 and 4 aren't as good (but good nevertheless), but they were ported by competent people.

Havent played it in a pretty long time but Lords of the Realm. You can have a 2 player on the same machine and i think you can get games going online but might need something like hamachi. Interesting thing with LotR is you normally work co-op to get rid of the npcs but you have to plan ahead for slaughtering your buddy.

The first Age of Wonders does at least work just fine (it's my personal favourite in the series)

You might also want to take a look at something like Crusader kings 2, Europa Universalis IV, Victoria 2 or Hearts of Iron 3. They can be played cooperatively. And if my memory serves, Commands 2 also has a co-op mode.

Hammerwatch is pretty nice for co-op. It doesn't really fit to any of your favorite genres but It's neither in least favorite genre list so I can suggest to give it a try. Actually this game is more or less designed for co-op, playing it alone is not that funny.