There are non-profit organizations that collect bikes for people living in poverty, either in this country or overseas. They take working or broken bikes, as well as bike parts, and use them to fix up bikes for people who need them. If none of the places listed below is near you, you may be able to ship your bike to one of them.
Working Bikes Cooperative, Chicago, workingbikes.org
Bikes Not Bombs, Boston (bikesnotbombs.org
Pedals for Progress, High Bridge, New Jersey (p4p.org
Bikes for the World, Washington, D.C. (bikesfortheworld.org
Bikes Across Borders, Austin, Texas (bikesacrossborders.org