Update May 2009: The recently-passed stimulus package included massive funding for research, which could result in more opportunities for you to serve as a medical research subject.
Most large universities have ongoing medical research projects evaluating the efficacy of new medicines and treatments. As part of this evaluation, they often need 'volunteers' on which to test these medications. Since the pool of willing volunteers is limited, cash compensation for the volunteer's cooperation is sometimes provided, ranging from a few hundred dollars up to four figures.
Among the opportunities I found on a quick check: The National Institutes of Health has 300 studies that need volunteers. The Rochester Clinical Research is looking for volunteers to test an Avian Flu vaccine. Google medical test volunteers for more.