Much as I'd like to be, I'm just not a fan of most modern African music. With few exceptions (Malian music for instance), it just doesn't do it for me.
What I really love, though, is African music from the 1970s, particularly from West/Central Africa and Ethiopia. This podcast of a European radio show called Radio Freetown (with free downloadable archives!) plays mostly obscure but great 70s West African music. In terms of individual musicians, Fela Kuti is the superstar of this era; his song "Zombie" has been credited with playing a role in brininging down one of Nigeria's military regimes. The Ethiopian musician Mulatu Astatke (whose music was featured in Jim Jarmusch film "Broken Flowers") haunting organ music is fantasic and unique. There is a record label called Soundway that releases a lot of compilations and reissues of this kind of music, the "Nigeria Special!" albums in particular are excellent.