Lately, my historical curiosity has directed me to learn more about the history of sub-Saharan Africa. I am already aware of "Guns, Germs, and Steel" by Jared Diamond and "King Leopold's Ghost" intend to read them at some point in the future. What other good books are out there that go into sub-Saharan African history. Books that go into pre-colonial times would be even better.
Also, I would mention that I'm lukewarm on Guns, Germs and Steel.
There is a section in the FAQ devoted to critiques of GG&S. Beyond those criticisms, I don't really think the book is "about" African history, per se. Diamond only engages with Africa in comparison to Eurasia, and with the purpose of explaining why Eurasia had "advantages in development". I don't think he really tries to describe how African societies changed over time, and he isn't really interested in Africa on its own terms.
In addition to the book list that /u/EsotericR listed, I'd also throw in a few suggestions not listed.
I like History of Central Africa Volumes I and II, edited by David Birmingham and Phyllis Martin. Volume I covers the pre-colonial history of the region, Volume II covers the colonial era. I haven't read Volume III (the post colonial era up to 1996).
Archaeologists have done quite a lot of research on pre-colonial African societies, and I find Graham Connah's African Civilizations; an Archaeological Approach is a good introduction that touches on a few of the outstanding urban civilizations. It gets a bit into archaeological jargon in parts, but on the whole is pretty readable to the non-specialist.
African Archaeology; A Critical Introduction edited by Anne Brower Stahl is somewhat more involved in anthropological/archaeological theory, is drier, and requires some greater grounding in archaeology and anthropology. Still, it provides a wider scope than Connah, both in time-depth as well as exploring forager societies and middle range societies in addition to the very complex urban societies.
The Africa section of the Books and resources section of the Wikihas some excellent suggestions to get you started.
Of the books on the list, I personally would recommend John Illife's Africans. It's accessible to most readers and provides a broad synopsis which might lead a reader to more specific areas that they are interested in.
Sub-Saharan African history tends to get very regional in the pre-colonial period, generally divided between South, East, West and Central, with a lot of texts focusing on specific areas within those regional distinctions. If you can give an idea which areas or themes you're interested in (for example the Congo with Kind Leopold's Ghost) I can recommend some more specific texts. If you're not sure you could try Jan Vansina's Kingdoms of the Savanna which covers pre-colonial central African Savanna states. It is a more academic text than the two you have mentioned and might be harder to get into with a historical back ground, but there are a fair few copies in circulation so it shouldn't be hard to find.
The challenges of Africa by Wangari Mathai is a good one