Here is one.

Here is another.

I really love this question. I have a couple weak answers because you can participate but probably not in the fashion you were imaging—and by that I mean you donate computing time from your computer to help with medical research and locating intelligent alien life:

1. http://folding.stanford.edu/
2. http://setiathome.ssl.berkeley.edu/

In terms of technological research there’s a lot of communities like http://diydrones.com/ where there’s a lot of people doing primary research and supporting research into some of the most advanced navigational systems out there.

Moon Zoo may be more assessable.