Various people have had the bright idea to use this spare capacity to solve difficult problems. One of the best known projects is SETI@home that analyses radio signals for signs of alien intelligence. I ran that briefly, but have dedicated much more time to distibuted.net (mathematical proofs and code-breaking challenges) and grid.org (medical research). I've clocked up several years of processing for each of them.
I don't get paid for this or anything, but I like the feeling that I am contributing to possibly worthwhile causes. I've recruited others to the cause and am always trying to bring in more people. For grid.org I started a team called Whizz for atomms (a Gerald Searle reference). Feel free to join us.
I know some people will worry that these programs could pose a security risk, but I'm very wary myself. I check various forums for any potential issues before installing anything. I've not heard of issues with either of these. Some people have found that they can affect their PC performance, but I've not noticed this. Mail me if you have questions.