Why do we play?

This thread on The Miniatures Page (which subsequently devolved into the usual "Someone is WRONG on the internet!") has an interesting theory on how our reasons for playing games can be classified by four categories, as show in the diagram above, which came from that thread.  From the original post:

• Immersion: The player enjoys being immersed in the game narrative, the pretending. They want to experience another time, cultural or challenge apart from real life.
• Cooperation: The player enjoys the social aspects of playing games, the camaraderie. It may not matter what game is played as long as there is good company.
• Achievement: This is about accomplishment, but not necessarily winning a competition. It can be mastering the game system, finishing that 2,000 figure army or setting up a beautiful table or painting an outstanding stand of miniatures.
• Competition: This is about winning. Tournament play looms large in this quadrant, but simply playing the game to win is a large part of the enjoyment. This doesn't mean 'win at any cost' or 'rules lawyering', but simply playing the game as a competitive challenge.

I play different games for different reasons.  For example, with Hordes of the Things, its for both achievement (building a cool-looking army) and competition.  But there is also the cooperative aspect of getting together with friends for a  tournament or campaign, and campaigns also result in a bit of immersion.

My spaceship games, on the other hand, are more for immersion and cooperation, although the achievement of running games and campaigns (as well as assembling and painting fleets) is also a big draw--but I don't care about winning that much, as long as everyone has fun.

So what draws you into gaming?  Is it just one thing, or a combination?  And does it change with the game?