Check in your area for bike co-operatives, earn-a-bike programs, world bike programs, bike kitchens, bike labs, etc. Most of these programs depend heavily on volunteers, many will train you in basic mechanics if you volunteer.

I volunteer at Bikes-not-Bombs in Boston. Every Wednesday night I get to strip a bike, usually a cheap beater, but some top-end, older Treks, Specialized, and Bianchi. It really drives home the importance of regular maintenance of every connection on a bike. Taking a bike apart is 3/4 of the way to putting one together. As a volunteer in the earn-a-bike program, I get to help kids take apart their donated bike, evaluate what needs to be replaced, replace it, reassemble and then do any needed adjustments. It is really nice to help kids learn these things and get involved in cycling. It is my way of giving back to the cycling community and community at large, while doing something I enjoy