I've been travelling all over Africa on business for 25 years and I've a few thoughts on the subject, as you might expect!
One of the biggest problems is the "Big Man" complex where you are not respected unless you are ostentatiously wealthy with cars, cellphones, mistresses and wads of cash. Most Africans can't afford this lifestyle so the temptation to steal is overwhelming. Add short-term thinking into the mix and you can see why in Nigeria for example everything operates on bribes with no consideration for the long-term effect; you have senators who are paying themselves several million dollars a month from the public purse, grabbing what they can for now with no thought for the consequences because they don't know where they will be tomorrow. Public contracts go not to the most efficient bidder but to the bidder who offers the biggest kickback. A good example of short termism is the almost complete lack of any electricity supply in Nigeria: the reason is that ministers get fat from kickbacks from the importing of generators so they have no reason to set up any programme of investment in a public supply, with a ten-year investment cycle in power generation they will almost certainly be out of their jobs by the time it might be possible to profit from the investment.
Religion: African Christians and Muslims have a fatalistic belief in the will of God, meaning that any misfortune is merely accepted as God's will with no attempt to rectify the problem. Religion also has a detrimental effect on development; in northern Nigeria polio is thriving because the mallams in the mosques tell people not to let their children be inoculated because the inoculation is a US-funded plot to sterilise them and stop them having kids.
Lack of education is the principle hindrance to development; intellectual flight means that anybody with a decent brain leaves Africa and takes their expertise elsewhere. This affects white South Africans as much as black; much though I like white South Africans I find them mentally lazy and almost childishly naive at times.
There are a few rays of hope: presently Lagos state has a good governor called Fashola who is thought not to be chopping all the money. Consequently some money is being invested and it's remarkable what a difference this makes when a city is as bad as Lagos once was - the streets are being cleaned and there is street lighting, traffic lights and investment in new roads and bridges meaning that life is less awful than it was ten years ago. This kind of public investment attracts private money so there are new hotels, new malls and restaurants appearing in Lagos, all of which has a knock-on effect on the local economy.
In South Africa the premier of Western Cape province, which includes Cape Town, is a white protestant Afrikaaner named Helen Zille who runs the state by the book and consequently Cape Town is a city which works; there's reasonable security, investment and companies are happy to remain in the city meaning there's employment, people in the streets and cash in circulation.
There are other small pockets of hope, I haven't been there since the war but I've heard that Rwanda is being run correctly by the president and that consequently there's security and money and the country is doing well. If Rwanda can improve the level of education it will be on the road to recovery. Meanwhile people say that one of neighbouring Uganda's biggest problems is the general lack of education caused by former governments' fear of creating an educated middle class because these are the kind of people who object to malpractice and cause political instability.
Obviously these are just a few random thought on the subject; anybody who travels to Africa has their own ideas and the problem is massively complex.