I can't believe no-one has mentioned this one. On many an occasion I've removed the ball from a coworker's mouse and watched in amusement as they shake and jiggle it trying to make the cursor move. You can acheive the same effect with a piece of opaque tape for the newer optical mice. Ah, life's simple pleasures. :)

I've had a similar thing happen on older PCs. I put it down to electromagnetic emissions from the CPU/RAM/whatever being picked up by the circuitry driving the PC speaker, which amplifies it into that annoying buzzing noise. Try disconnecting your speaker and see if the noise goes away!