The Berkeley Open Infrastructure for Network Computing (BOINC), an open-source middleware system that supports volunteer and grid computing. Originally developed to support the SETI@home project, it became generalized as a platform for other distributed applications in areas as diverse as mathematics, linguistics, medicine, molecular biology, climatology, environmental science, and astrophysics, among others. BOINC aims to enable researchers to tap into the enormous processing resources of multiple personal computers around the world.
Milkyway maps a 3d map of the MilkyWay for future space explorers
Primegrid finds primes
GPUgrid uses memory cards for various university physics problems and models
SETI is looking for aliens
WCG finds cures for various diseases, protein modeling, and water filter efficiency testing
Einstein is various physics modelling for universities
Cosmology is astrophysics models
LHC is from CERN, physics
Collatz is maths
Asteroids tracks replies from satellites tracking asteroids in space, 3d maps them
Rosetta protein folding and 3d modelling
vLHC more CERN stuff
TN-grid and POEM are retired