The SETI Institute is one of the primary groups responsible for the continuing investigation into possible signs of extraterrestrial intelligence via analysis of radio telescope data. Founded by Frank Drake, the institute has been working for several decades to try and sift any seemingly intelligent signals out of the jumble of signals arriving from deep space, while also trying to filter out false-alarms generated by earth's own buzzing cloud of thousands of man-made satellites.
SETI's mission was popularized by the book "Contact" (ISBN 0671004107 (alternate, search)), by Carl Sagan, and then futher popularized by [the movie of the same name], starring Jodie Foster. These both alerted millions more people to the possibility that there may intelligent life "Out There".
You can find more about SETI itself at http://www.seti-inst.edu/ or http://www.seti.org/ (Both addresses go to the same machine, but it appears to be down at the time of this writing. Please update this page when the links work correctly, and remove this comment. Thanks!)
SETI@home is a distributed signal-crunching project that lets anyone with a computer and an internet connection participate in the search for possible signals coming from other civilizations. You download their software and a chunk of radio telescope data and let your computer analyze the data. Millions of people are currently participating, some of us for several years :)
Interesting Side Note: When the SETI@Home project was first envisioned, the folks at SETI thought that if they could get up to 50,000 personal computers working on data analysis, they would surpass the computing power of the largest parts of the existing SETI project. They passed 50,000 probably within the first few days, and have rocketed on to levels no one even dreamed of. As of Sept. 19, 2002, the project has had 3.977 million users, with approximately 550,000 people still remaining active. Together, these computers have donated 1.135 million years of computer time in the search! (Now if we could only find some aliens! ;^) )
More information and the software can be found at http://setiathome.ssl.berkeley.edu/
And if you decide to help look for aliens, [Reality Sculptors has its own group that you are invited join.] It's listed as a Club and is called, of course, 'Reality Sculptors'.