Owners of Android devices carrying Android 2.3 or greater can donate their spare computing cycles to a number of different projects (screenshot above) via the BOINC app in the Google Play Store. We can already hear the questions about how the app will affect battery life. Any such degradation will be minimal, as devices running BOINC will only participate when all the following conditions are met: It is charging, connected to wi-fi, and the battery is already charged above 90 percent.
The BOINC project, by the way, was founded at the University of California at Berkeley in 2002, with support from the National Science Foundation.
Notably, BOINC is also behind SETI@home, but that project is not listed among the projects you can participate in (but projects can be added via URL). In the astronomical vein, though, are Einstein@home and Asteroids@home. Einstein@home currently has over 340,000 participants worldwide, and is already responsible for discovering nearly 50 new radio pulsars.
Through IBM's World Community Grid, you can also plug your device into the FightAIDS@home program. The Grid has already been used in projects that include researching cures for malaria, cancer, and other diseases. There are already over 2.3 million computers plugged into the grid with 600,000 people and institutions from 80 countries being used to accelerate over 20 projects.