Most of those grid projects are for medical research and protein folding experiments. I personally run Folding@Home, which simulates the folding of proteins. I guess they are trying to learn a couple of medical things with this--they think it will lead to discoveries about Alzheimer's especially.
Unfortunately, most people who are donating their CPU cycles are doing it for SETI, which searches the cosmos for intelligent life (I personally think the medical cause is more important, but I am in the minority).
It's a good excuse for me to overclock my computer, anyway. Brings out the geek in me.
My computer is trying to cure cancer
right now. What is yours doing at night? If you leave it on all the time but don't participate in folding, some would see this as a crime!
But interestingly, my friends who leave their computers on all the time refused to install Folding@home. Huh.
Anyway, if you're interested in helping medical research:
Folding@Home Distributed Computing