Your school may have clinical programs abroad (ours has a Global Health program that includes clinical experience and research in places like Tanzania, China, etc.) Outside of your school, summer fellowships are offered by professional societies or other organizations / hospitals, e.g.:
Pediatrics: APS summer research program
Anesthesia: FAER summer program
HHMI summer program
Gold Foundation summer program
...and about a bajillion more, check this page: http://www.med.upenn.edu/mdresearchopps/shortterm_opps.shtml
I did the FAER summer program, knowing that I wanted to do anesthesia. Learned a ton, met a lot of leaders in the field, got a paid trip to the annual conference in San Francisco and gave an oral presentation on my work. This yielded an abstract, a LOR, a meeting with the PD of the program I was working at, and it was a really fun experience. Lots of people tell you to lay on the beach all summer...which sounds cool, but this way you're getting paid and can still take weekend trips since research hours are relatively light.