One Deck Dungeon - you work together to fight the monster on each card using your dice. You have to plan the move together so that you will win. It's a lot of fun.

Blue Moon. We have the Legends version with a million or so cards. It's definitely a competitive one. You build a deck, increasing your firepower (hopefully) as you go, and battle your opponent's deck each turn.

It took us a while to figure it out but man is it fun to play once you get the mechanics of it. Even teenage boys who had been rolling their eyes at the game for weeks tried it one day out of boredom and became obsessed as soon as they figured out how to start backstabbing each other.