Great (Local) Multiplayer Games - Xbox 360
I don't really like single player games, but when I've got some friends over, playing video games is one of my favorite ways to pass the time. What I've found, however, is that just saying 1-4 on the box doesn't mean that it'll be an enjoyable experience, even if the single player mode is great. (Likewise, you may find a few single player games on here, if they lend themselves well to taking turns.) Add your own!
Note: The reason I've added the "local" caveat is partially because that's my preference and mostly because local multiplayer is always an option, but support tends to end for online sooner or later, and I want this list to continue to be useful indefinitely.
Lists for other platforms: