They're not missions in the religious sense, but Wisconsin has a program where students can spend a couple weeks at various sites in developing areas (Belize, Thailand, maybe Mexico... there were five or six of them). It's partnered with the medical (and nursing? and public health?) schools so the group is really going down there to heal the whole community, give them strategies for disease prevention, sanitary practices, livestock management, ecosystem health, etc. Sounded like a pretty cool program - there's funding available too, so you might not have to pay for it.