Coop
Fail with friends
In a cooperative game all players work together with shared goals.
Mechanics
Shared goals & outcomes
Inter-dependant roles
Shared resources
Couch / Online
A game that has multiple players using the same system is called a couch co-op or a local co-op games. If each player has it's own system it is called an online co-op or multiplayer co-op. Some games combine it and let more then one player on each system that also play online.
Split screen
Asynchronous co-op
Games
Saints Row The Third - 2011
Left 4 Dead 2 - 2009
SWAT 4 - 2005
Neverwinter Nights - 2002
Doom - 1993
Reference