Personally, I don't rely on the camera picking the right focus point as it can get it wrong and by the time I've gotten it to pick the right one, the moment (and my shot) is gone. I always pick one of the AF points myself.
Now... regarding people saying they use the centre point and then recompose. This might be fine under ideal conditions but if you're using a large aperture, focus and recompose can screw your focus in a big way because when you recompose you're changing the focal distance. If you have razor-thin depth-of-field and need to nail your focus, recomposing the shot with the focus locked in will mess things up royally. There's a good article about it here:
http://visual-vacations.com/Photography/focus-recompose_sucks.htm
It's a pain having to keep switching AF points but it's worth it if you have to use a large aperture. Takes a bit of practice but it's pretty easy on Canon systems at least as the AF selection button is under your thumb and you can change it with the dial quickly. Just a shame that the spot metering zone isn't tied to the AF point on most Canon systems but that's another discussion altogether.
George.