As of my visit in 1998, Kenya, Tanzania and Zambia required Americans to have a valid visa as well as a passport. I was very satisfied with Zierer Visa Service . I sent my passport to them by Federal Express and they hand carried it to each of the necessary consulates in New York. If you need several visas, it is not a trivial expense. Also, make sure you leave enough time to get the necessary visas.
Some consulates are slower than others.
These copies should be kept somewhere separate from the originals. Such copies can be very useful in the event the originals are lost or stolen. The only incident I heard about was that a fellow in one of the groups had a gold chain snatched from his neck while walking the streets in Nairobi. I never experienced or heard about any thefts in any of the camps, even though many people had rather expensive photographic equipment, binoculars and other items. Nevertheless, it is never wise to tempt fate.