There’s been a great trend in boardgames lately toward cooperative gameplay. Instead of screwing each other over every 30 seconds (Sorry!) or acting like a New Jersey slumlord (Monopoly), all the players cooperate to beat the rules of the game–either everybody wins, or nobody does. Probably the best example of this is Pandemic, a game in which each player has a different role in a small team trying to stop the outbreak of plagues across the globe.
Other good cooperative games include Forbidden Island, Defenders of the Realm, and Arkham Horror. “Adversary” games, in which one or two players end up working against the others often use similar mechanics: Fury of Dracula, Battlestar Galactica, Last Night on Earth, Descent, and Betrayal at House On the Hill. One advantage of such games that I’ve not heard mentioned by others: it makes a game much easier on new players. Everyone else really IS trying to help you, and it’s in their interest to offer their best advice when it’s your turn. I don’t know if it’s because such games are innovative by their very nature at this point in history, but I’ve yet to play a co-op game I didn’t like. So boardgame players, especially those of you with children old enough to play, get thee hence to your FLGS and pick up one of the co-op games I linked to above; you won’t be disappointed.