This weekend, I played Scotland Yard, a cops-and-robber game, in which one player, Mr X, is pursued by the other players, the detectives. This game is awesome, because Mr X wears a visor. The rule suggest playing with at least four people.
The detectives have a perfectly shared objective--if only one of them apprehends Mr X, they all win. It's a pain to get four people together, so games that say that they need that many people ought to have mechanics that make each one important. Scotland Yard works just as well with two people, with one taking the role of several detectives, acting as several players, if you will. (Now, as Mr X, I found it fascinating to hear the conversations of four people plotting against me, but the way the game was played, there was no need for an actual one-to-one correlation between people and detectives--the players agreed on what each detective would do.)
The first time I ever went to the Collins Avenue Thrift Store, I paid $3.46 for the Lord of the Rings board game by Reiner Knizia. In LOTR, the players play as the Hobbits from the books, Frodo, Sam, Pippin and Merry. Fatty is thrown in, too, for good measure, so up to five can play, working together to throw the ring into Mount Doom. It's fun, but I normally play it solitaire, acting as five players--it works better that way. The only reason I'd want other people involved is for help with strategy. I have five Hobbit playing tokens, but I can manage all of them myself.
In Star Wars Risk, the four players play as two teams of two, and the game is broken otherwise. I prefer to play Star Wars Risk with a single friend, and we each handle a team of two players. Just because the game rules call for four players doesn't mean four people are needed to manage them.
This effect even shows up in some competitive games: I have no idea why people bowl as a social activity. You get the same gameplay if you're bowling alone as if you're bowling with others. Golf is the same way. I think darts is, too. The only reason you do these things with other people is because you like them. Croquet is unusual, in that it's a mellow skill game that actually gets better with more players.
Bang! is one of the rare games in which players cooperate, but in which you need actual people to act as each player. Many compare Bang! to Mafia, as each player is given an objective, but no one knows what roles the other players have taken. In Bang!, the sheriff and his deputies face off against a band of outlaws; a couple of renegades are thrown in for good measure. Cooperation is required, but because one doesn't know who is on one's team, it's not the sort of cheap cooperation seen in Scotland Yard, Lord of the Rings, or Star Wars Risk.