There are a couple of ways you can donate your computer's downtime, or unused CPU power, to benefit science. One way is SETI @ Home, which is a scientific experiment based at UC Berkeley that uses internet-connected computers to search for extraterrestrial intelligence. You just install it on your computer, kind of like a screen saver. Whenever you're not actively using the computer, it will work to analyze radio signals they're collecting. Find out more at setiathome.berkeley.edu
Another one is Folding@Home, based at Stanford Univeristy. This is focused on disease research. In this case, "Folding" refers to the way human protein folds in the cells that make up your body. When the misfold, there can be serious consequences to one's health. This distributed computing project simulates the protein folding, computational drug design, and other types of molecular dynamics. Find out more at foldingathome.org.