Unlike all other mice that have a small wheel spinning around an axis, Apple's Mighty Mouse has a scrollball that transmits the rotation via friction: so when the ball gets dirty or when particles get into the internal hardware, the mouse doesn't scroll any more.
The solution is just: clean it!
Seems like a pretty common problem, and Apple published a KB article that explains how to clean the mouse, emphasizing on how to clean the scrollball: How to clean your Mighty Mouse.
They also published a quicktime movie that shows you how to properly do it.
And if cleaning with a cloth is not enough, some suggest to insert a piece of paper to help remove the dust.