I have used REI Adventures last year to go to Africa - guided hike up the Kilimanjaro Mountain. The trip was pricy however, I think the cost and trip was worth every penny! Everything was taken care of for the group, from the pick up at the airport, taking care of obtaining visas for the stay in Tanzania to getting to the hotel, preparation for the hike and the guidance and care during the hike. The guides, the helpers- everyone was tremendously helpful and made the the trip an extraoridinary experience. I'd highly recommend REI Adventures!
Other companies I have heard about are Adventure Unbound and AdventureWomen but I have not done any trips with them so cannot give more insight.