There is a plan by one of the faculty members at Wayne State to start an annual 1-2 month elective experience at a clinic in Africa (I think in Kenya). This isn't up and running yet, but he's committed to the project (don't know his name).
Regarding doing this in private practice...while I don't disagree with orthodoc's statement, it should be noted that it is a generalization.
If you stay in academia you should be able to find a position willing to let you go for extended periods during the year (all the better if you work with an academic center in the developing country...the academic link would look good, plus you would be able to work in an equipped hospital istead of a hut).
Also, if you are very flexible in choosing a practice location, you should be able to find a group with other members who have motivations or interests that draws them away for extended periods during the year, such that different members may be gone at any given time.
PM me if you like as I am seriously banking on one of the two plans above to work out during my career (I'm very interested in relief work).