For information on donating a bike, see the home page or email 
Otherwise, [modified from ibike.org]:
Please recycle unuseable bike parts yourself....Unfortunately, most of the time people are shedding parts that are pretty much beyond "useable". Depending upon the items there are different preferred actions:
Aluminum parts: Rims, especially have been given second lives as furniture (see Resource Revival and Bike Furniture Design). Even if you don't have the hankering to be a craftsperson, or get the materials to someone who is, there is still enough value in aluminum that it is often cost effective to separate it out and take it to a metal recycler.
Tires: JaiTire, 3417 Girard NE, 505-830-2765. They charge $0.50/tire.
Inner tubes: Inner tubes have a lot of secondary uses before they need to be discarded. Generally they are great for "tie-downs". Inner tubes can be used for tying loads to racks, or trailers or hanging things from the ceiling. They have also been used as webbing for chairs, rugs (see the bicicleta model), and purses and bags. Pedro's USA has been collecting used inner tubes (Jan 2003). Send them to: Pedro's USA, attn: tube recycling, 600 Research Drive, Wilmington, MA 01887. For the latest details contact pedrosmail@pedros.com
Chains, chain rings, etc.: Local artists may be interested -- ask around. They find uses for things. Also, there are instructions floating around the Internet on how to make crafts like belts and wallets from busted tubes and picture frames from chains. If you have exhausted your local options you can check with Resource Revival and Bike Furniture Design.
Residual: The best you can do with the residual is try to steer it to a metal recycler. For the to accept it the item will need to have all of the rubber and plastic removed. You will need access to socially minded free labor to make this very worthwhile.