Partners in Health has many opportunities for volunteers. They are based in Boston but have operations in Haiti,
Lesotho, Malawi, Peru, Russia, Rwanda, the United States, the Dominican Republic, Kazakhstan, Mexico, Guatemala, and Burundi. I looked at some of the volunteer opportunities and all the ones I looked at required experience.
to go to their volunteer info page.
International Volunteer Programs Association
Here is a list of organizations that use volunteers:
International Medical Volunteers Association
Many do not require experience and religious affiliation (or not) is also indicated.