The one I've played that's, in my opinion, the most fun is Betrayal At House On The Hill, a game that somehow manages to be cooperative and extremely paranoia-inducing.
Each time it's played a small group (3 to 6 people) wander into an old house. You know the type. It's on a hill, it looks like nobody's lived there for ages, the yard looks like it's completely run down. The inside of the house is never the same, and each time things turn dark for the players, it's never (exactly) the same game twice.
Instead of a single game board, the "board" is made up of tiles that can be connected to certain floors of the house. Tiles are drawn randomly, and certain rooms are more foreboding than others. Certain rooms contain items that can be picked up, others have events or omens happen in them each time they're discovered.
|Ominous things happen in a dining room? What is this, Clue?|
For the most part, people attempt to work together to explore the house. You don't want to get too far away from other players, and people are encouraged to swap items that might be more beneficial for one person over another.
However, the game has a twist. As omens make themselves known, people need to roll dice to determine if "the haunt" has begun. There's a table that keeps track of what room people were in and what omen triggered "the haunt," and that's when everything goes crazy.
Sometimes, the house just flat-out tries to kill everybody, and all of the players attempt to work together to survive.
More often than not, however, one of the players gets assigned the role of "traitor." They work with the house to kill all the other players. Maybe there's a giant serpent in the basement that the traitor wants to feed everybody to. Maybe there's a pentagram that needs a ritual completed before a certain time and the other players are to be the (unwilling) sacrifice to it. Maybe the house is just alive, and the traitor wants to make sure no players leave with that knowledge.
A game that manages to be both "player versus player" as well as highly cooperative, it's rather amazing how having a face you can attach to all the bad things that happen in the game to twists it around from simply being dumb and silly into being something suspenseful and dramatic. The players who aren't evil are never really sure of what the traitor's end game is. The traitor usually has a limited time frame or resources to get his goal accomplished. It becomes a competition and wits as one group of players attempts to scheme and plot to foil the schemes and plots of another player.
And (unless you happen to play in my usual group), it's often not always the same player who winds up facing against all the others.
This change and randomness makes things more difficult the more you play the game. Initially, you might want to keep everybody in good shape so that everybody's healthy and ready to fight against the house's forces. However, maybe you realize that this time you're playing someone who's physically weak, but you find an object that will heal someone. Another player gets injured before the haunt begins. Do you use your healing object on them so they're less likely to die when the haunt begins, or do you hold onto it unless they (or you) winds up being the traitor? Keep playing, and you find yourself constantly trying to work out "what, in the long run, would be best for me?"
After all, it's not like everybody needs to survive the house, usually it only matters as long as one does.
Now, wouldn't it be neat if that survivor was you?
If you want a great indication of just how much fun this game is, I recommend Wil Wheaton's Tabletop Series which spent a couple episodes going through it.