For general sources of statistics, please see our guide on International Data: http://libraries.iub.edu/data-international-statistics
Stanford University has also compiled a thorough list of sources for African Statistics.
Most countries have a national statistical office, but these sites are not always easy to navigate, and may not have an English language option. The United Nations maintains a very helpful list of their websites: http://unstats.un.org/unsd/methods/inter-natlinks/sd_natstat.asp
If you need general, or regional data, some great places to start are:
A few Africa-Specific Sources
See also: Stanford's list of spatial data sources for Africa and list of digitized maps