This is the way to go where there's a good network of sealed roads. International bus services are pretty common across the continent, and in the wealthier African states you may get a choice between 'luxury' air-con buses, with movies (the trashy Hollywood/Bollywood variety) on tap, and rough old European rejects with nonfunctioning air-con and questionable engineering. In some countries you just get the latter. Out in the sticks, where there are very few or no sealed roads, ancient buses tend to be very crowded with people, livestock and goods; these buses tend to stop frequently, either for passengers or because something is broken.
Small minibuses take up the slack in many African transport systems. All too often they are driven at breakneck speed and crammed with close to 30 people when they were designed for 18 (there's always room for one more), with a tout or conductor leaning out the side door. The front seat is the most comfortable, but thanks to the high number of head-on collisions in Africa, this seat is called the 'death seat': how many old bus-drivers have you seen? (If you do see one, be sure to choose his bus!) These minibuses are known by different names across the continent (matatus in Kenya, dalla-dallas in Tanzania, tro-tros in Ghana, poda-podas in Sierra Leone), names that are, confusingly, fairly interchangeable for shared taxis and bush taxis. Minibuses usually only leave when very full (a process that may take hours), and will stop frequently en route to pick up and set down passengers. Minibuses are also the favourite prey of roadblock police, who are not averse to unloading every passenger while they enter into lengthy discussions about paperwork and 'fines' that may need paying.
Shared taxis are usually Peugeot 504s or 505s or old spacious Mercedes saloons (common in North Africa). They should definitely be considered, where available (which is not everywhere). Your average shared taxi is certainly quicker, more comfortable (if a little crowded) and less of a palaver than taking a bus or minibus, although many shared taxis are driven by lunatic speed freaks. They cost a little more than the corresponding bus fare, but in most cases once the vehicle has filled up (usually with nine to 12 people, packed in like sardines) it heads more or less directly to the destination, without constant stops for passengers. You should expect to pay an additional fee for your baggage in West Africa, but usually not elsewhere. Motorcycle taxis can also be convenient, if dangerous.
'Bush taxi' is something of a catch-all term and is used slightly differently across the continent. Basically, a bush taxi is any multiperson mode of public transport that isn't a bus.
In many out-of-the-way places, trucks are the only reliable form of transport. They may primarily carry goods, but drivers are always keen to supplement their income, so there's usually room for paying passengers. Most folks are stuck up on top of the cargo, but a few more expensive spots are often available in the cab.
Sitting high and exposed on top of a truck chugging through the African landscape can be a great experience; just take heavy precautions against the sun, wrap up against dust and bring a carry mat or similar to cushion yourself against uncomfortable cargo – you could find yourself sitting on top of a car engine for hours on end! Also, remember that trucks are even slower than buses.
On many routes you'll be able to wave down a truck, but lifts can often be arranged the night before departure at the 'truck park' – a compound or dust patch that you'll find in almost every African town of note. 'Fares' are pretty much fixed – expect to pay a little less than an equivalent bus fare, and make sure you agree on the price before climbing aboard. If the journey is going to take more than one night or one day, bring your own food and water.
Because most people prefer to travel north to south, overland truck companies sometimes drive empty trucks back from South Africa's Cape Town, Victoria Falls and Harare, and will sometimes transport travellers back up to Arusha (Tanzania) or Nairobi (Kenya) for negotiable knock-down prices, with a pleasant two-day stop by Lake Malawi sometimes thrown in. Ask around in backpacker hang-outs in the departure towns for tips on when these trucks may be leaving.