I didn't see this organization mentioned in any of the threads and a search wasn't successful (or useful) so I thought I'd mention it here.
From the organization's website:
"The National Association of Free Clinics (NAFC) is the only nonprofit 501c(3) organization whose mission is solely focused on the issues and needs of the more than 1,200 free clinics and the people they serve in the United States.
Founded in 2001 and headquartered in Washington, D.C., the NAFC is an effective advocate for the issues and concerns of free clinics, their volunteer workforce of doctors, dentists, nurses, therapists, pharmacists, nurse practitioners, technicians and other health care professionals, and the patients served by free clinics in communities throughout the nation."
I haven't had any experience with them but they are the organization that recently held a free clinic in Houston, Texas, that was widely publicized: 700 volunteers on a Saturday morning (9/26/09) saw 2,000 uninsured patients. According to the association's president, the NAFC treated 4 million people in 2008; they expect to see 8 million in 2009. Texas reportedly has the highest number of uninsured people in the country.
If you go to the website you can look up free clinics in your state. These appear to be permanently established free clinics, though the organization runs free clinic days in various locations around the country.