Problem: Large scientific computations require many computers in order to effectively process the data.
Solution: BOINC is a software system that makes it easy for scientists to create and operate public-resource computing projects. This allows researchers to distribute the computation to millions of regular computer users through a client-side platform that runs when the computer is idle. The paper describes features that went into BOINC to make it easy for scientists and attractive for users. Incentives for users are a nice interface and a count of how much they are contributing to the project (Top Alien Hunters).
Influence: I remember running SETI@home 24/7 in the background on my P3 600MHz overclocked to 800MHz.
Main project website: http://boinc.berkeley.edu/
Listen for ET’s call: http://setiathome.berkeley.edu/
Find gravity waves: http://einstein.phys.uwm.edu/