If you are looking for a Church based group Medicine on the Move is a great group doing work in western Africa. A good friend of mine is a pilot with them and loves the time that she has spent out there.
Angel Flight is a group that does medevac type flights all over the world and is a none profit group that i have heard great things about.
I work for a company called Angel Med Flight a for profit Medical transport, that has flies all over the world. Last I heard we are hiring a few more medics for part time work and in the next few months should be hiring full time as well.
Also there is also Medics without Boarders (I dont know as much about them but it is my understanding that they are similar to Docs without Boarders.
Good Luck and I hope that this helps.