I can't answer for Africa, or your specific query of Kenya, but I have worked a lot in some of the poorer countries of central Asia, and also, over the past few years I have spent a lot of time working in the Caucasus. Before that, I also spent quite some time in the Balkans in the years immediately after the Yugoslav war of the 1990s.
In general, my experience is that you will fairly easily find decent internet access and connections in the cities and towns - even in the poorest of countries, and the poorest regions of those countries. However, if you plan to travel to remote rural regions, the sort of regions with dirt tracks, no running water, and dismal living conditions, I very much doubt that there will be any sort of internet access. I can imagine 3G being available in the cities, but it may be a bit optimistic to expect it in the countryside.
In recent times, knowing internet access could be hit and miss in remote areas, I have bought a modem when posted abroad.