There is a lot more to medevac then just plucking hurt people out of the woods with a helicopter. For example you have Medevac transport maintained by the Air Force, where they retrofit cargo planes with Litters and airlift multiple patients out to a more capable facility. You see this a lot with our present operations in the Gulf and Afganistan. They used to have the C-9 as a sole medivac mission aircraft (on which my father spent many a day) but that has been farmed out to other aircraft. If you mean what groups do missions as primary Search and Rescue, your best demand would be with the coast guard. I think we have one or two coasties floating around this forum somewhere, but I cant remember their names. Also the AF PJ units maintain a high capability for Combat Search and Rescue, many are stationed up in the New England area to both train in bad conditions (ever been to NE you'd know) and to augment civilian capabilities in time of need.
There are still a couple of Medivac units in the AF stationed in differnt places. Cant really speak for the Navy side, since thats not what I grew up in. My father was Air Force, hey we all make mistakes sometimes.