Years ago, I participated in SETI@home, a massively distributed computing project by the Search for Extraterrestrial Intelligence program. Millions of ordinary people contributed their idle computing power to process the vast amounts of data that SETI collects. Distributed computing has expanded since then.
This site tracks many distributed computing projects–past, current, and upcoming.
Some examples:
Evolution@home “is the first public global distributed computing project targeting evolutionary questions by distributing the work to many PCs like the SETI@home and other similar projects . A central server distributes the work to those computers who want to participate in their idle time. So, while you are sleeping at night, your computer will simulate the effects of various evolutionary factors. . .on the survival of populations of endangered species and. . .on the evolution of novel functional adaptations.” (For the more technically minded, see the paper here.)
“The Virtual Laboratory project is engaged in research, design, and development of Grid technologies that help in solving large-scale compute and data intensive science applications in the area of molecular biology. . . This helps in examining/screening millions of chemical compounds (molecules) in the Chemical Data Bank (CDB) to identify those having potential use in drug design. “
ZetaGrid aims to verify Riemann’s hypothesis which states that “all non-trivial zeros of the Riemann zeta function are on the critical line (1/2+it where tis a real number).” (This is for those who don’t care if they really understand what they’re trying to help.)
Similarly but easier to understand, this project takes a stab at the Goldbach conjecture, which states that ever even number larger than 2 can be expressed as the sum of two primes.
Here’s a good two part article on distributed computing and the technical issues involved with implementing it.