Megan McArdle asks this question more colloquially.

there’s a whole, very large literature on why Africa is particularly screwed up. The awful climate under which most of it labors. The bad maritime geography: apparently one of the two coasts offers extremely little scope for building ports, the rivers don’t go where you want them, and when they do happen to meander near something interesting, they are hard to navigate. The huge patchwork of ethnicities. The bad borders–in Asia, borders were drawn somewhat along ethnic power lines, whereas in Africa, they were drawn mostly to suit the convenience of whatever western country wanted to do business there after the colonian powers left, and there is an emerging literature indicating that border that cut across ethnic lines are a recipe for conflict, and thus poverty. The unique medical problems of Africa…

Roughly speaking, I would classify the factors that have been introduced into the discussion into the following categories:

1. Physical factors, including transportation difficulties and climate.

2. “Top-down” institutional factors, such as poorly-drawn colonial borders, or corruption reinforced by the “resource curse” and the “aid curse” (unearned wealth tending to foster corruption more readily than earned income).

3. “Bottom-up” sociological factors, such as bitter ethnic rivalry or low IQ.

At last Friday’s Cato luncheon featuring Gregory Clark, Clark emphasized that settled agriculture is a much more arduous lifestyle than hunter-gathering (he said if he had to be tossed back in time prior to 1800 he would rather be placed in a hunter-gatherer society than in an agricultural one). To get the same amount of food, the civilized farmer has to work a much longer day.

When a modern factory becomes available, it’s not such a great stretch for a farmer to adapt. But for a hunter-gatherer, the long work day and monotonous nature of labor are really alien. Thus, it was much easier for Japan or China to eventually industrialize than it has been for Australian aboriginals or for Africans.

UPDATE: lots of good comments. Some folks, who seem to know more than I do, say that Africa had mostly settled agriculture. Also, some links to interesting sites, such as a chart ranking the institutional quality of sub-Saharan African nations (Botswana is #3, Zimbabwe–as of 2005–is 31, ahead of 17 others)