The University of Chicago has a peds team that goes to Honduras every year. It's a plastics attending and fellow and one of our peds anesthesiologists and one resident. Also, for the last couple years, we've had a resident go away for a month on the SEA/Katz fellowship. I think one went to Peru and the other to Tanzania.
Off the top of my head, I believe Vanderbilt and OHSU both consistently sent teams on medical missions. UCSF (according to what they told us) has away-rotations you can do abroad. When I did an away rotation at UNC, there was a group that had just returned from Guatemala.
So I think it's not hard to find it. From what (little) I know, it seemed like some programs counted it towards electives, while others made you use vacation time depending on what you were doing and how it was set up.
During med school I spent some time with a surgical team in Africa...enjoyed it so much that I made it a priority to find an anesthesiology residency that would allow me to do a little international work. I always asked about this in my interviews...and got a huge variety of responses...anywhere from "No, there are too many required rotations to allow room for international electives" to "Yeah, we have residents go abroad every year...we encourage and financially support these efforts." Some programs require you to use vacation time and come up with cash while others work it into your elective schedule, send attendings with you and fund the trip.
I don't remember the program-specific details anymore, but I do recall that Yale, Vermont, Pittsburgh, Utah, UNC and Dartmouth offered some sort of international experience. Michigan and Maine did not...though that was a couple of years ago so things may have changed.