I think cooperative multiplayer is more fun than the competitive kind. There's just something very fraternal about teaming up with a friend to achieve a common victory against the forces of evil. The Seiken Densetsu series is a good example of this, as are most shooters--Gradius Gaiden, Strikers, etc.

And there's probably no better bonding experience to be had in games than a co-op game of Quiz & Dragons.