Stemming from our discussion the other night, here is a list of the games we had considered for all of us to play:
(not all of these games can support all players at once, but they have a large backing behind their multiplayer funfactor)

Payday 2*
Evolve
Trine 2*
Counterstrike: Global Offensive
No Man's Sky
Orc Must Die 2*
Divinity: Original Sin
Splintercell: Conviction
Call of Duty: Black Ops (Nazi zombies)
Alien Swarm*

*these games are free-to-play or have a downloadable demo