One possible (though, to some, unpalatable) option would be to make it legal for organ donors to be compensated.
Drew Carey think that's a great idea. He hosts a video blog at Reason.tv (affiliated with the liberterian magazine of the same name). In this post, Carey makes the case for a free market for organs.
(Look! I got through this whole post without a The Price Is Right for Kidneys joke! Or a Whose Kidney Is It Anyway? joke!)