Given many of us on the road now carry smartphones (and laptops), it is fairly straightforward to get mobile internet using local SIM cards in virtually every Sub-Saharan country, and is generally comparable in price and speed to internet cafes but with obviously greater flexibility. Often the most difficult part is to get the appropriate network settings, which are usually entered somewhere in settings menu on the phone. Here's summary of our experiences so far along the Eastern side:

Ethiopia:
Only one company (ETC) but several non-GSM systems exist. Need to ensure that the correct GSM SIM is obtained, activated for internet, and language set to English at the ETC office – costs 85birr and requires copy of passport and two photos(!). Data packages are cheap but quality of service is poor.
Settings: APN: etc.com, username: < leave blank> , password: < leave blank>

Uganda:
MTN: good coverage and cheap data. No registration required to purchase SIM. Internet activation took 2 days, eve though the internet settings never arrived by SMS as promised. However, bizarrely, leaving all of APN, username and password blank worked. Orange an alternative with data bundles slightly more expensive than MTN.
Settings: APN: < leave blank>, username: < leave blank> , password: < leave blank>

Kenya:
Safaricom has good coverage, and mobile internet for 600MB for one month for KES 1000. Airtel has better rates and similar coverage – around KES 100 for 100MB or 100MB per USD, making Kenya the cheapest for mobile internet on our travels. Internet settings are (in case SMS with settings does not arrive on activation at the safaricom shop):
safaricom settings: APN: safaricom, username: <leave blank>, password: <leave blank>
airtel: settings: APN: ke.celtel.com, username: <leave blank>, password: <leave blank>

Rwanda:
MTN has good coverage and cheap data. Internet access needs to be activated after purchasing SIM (done on the spot at MTN shop).
Settings: APN: internet.mtn, username: <leave blank>, password: <leave blank>

Burundi:
None of our UK or Rwandan SIMs in roaming mode worked. Local SIMs (Leo widely used) available from U-com on the main roundabout at GPS: S3.381502 E29.361906 in Bujumbura
Settings: APN: ucnet, username: Ucom, password: <leave blank>

Tanzania:
Vodacom has good coverage with internet at TZS500/day for 20MB. 30 day packages available. Internet settings are:
Settings: APN: wap, username: guest, password: guest

Mozambique:
Vodacom has decent coverage but mCel is better in certain areas in the North e.g Ibo island. Vodacom has internet bundles at MZN49 for 125MB valid for 24hours, as well as weekly and monthly packages. For internet access to be enabled on Vodacom, dial *111# and follow the instructions. Even though the system tells you that your internet settings are being sent by SMS, they never arrived – seems to be a common issue. The following manual settings work:
Settings: APN: internet, username: <leave blank>, password: <leave blank>

Malawi:
TNM has unreliable coverage, especially for internet. Lilongwe is particularly poor for internet. Settings: APN: internet, username: <leave blank>, password: <leave blank>

Airtel is much better, and has the same internet settings as above, but needs activation by calling customer care on 111. Daily 20MB (+20MB bonus) bundle costs MWK 80.
There is also a wi-fi cloud service (SkyBand) in the main cities and hotels. Very expensive compared to mobile broadband from airtel/TNM, at MWK 700 for 50MB valid for 14 days.

Zambia:
Mobile internet is expensive. Both MTN and airtel pay as you go rates are approx MZK 1000/MB (or 5MB per USD), which is more than 10 times as expensive than elsewhere in East Africa. Airtel bundles are better, but typically require an outlay of USD25, valid for 30 days giving 300MB. MTN has no bundles. For airtel:
Settings: APN: internet, username: <leave blank>, password: <leave blank>

Zimbabwe:
Econet is widely used. Mobile internet using prepaid data bundles costs are around 10MB per USD.
Internet access needs to be activated at an econet shop/customer care. Internet settings are:
Settings: APN: econet.net, username: <leave blank>, password: <leave blank>

Botswana:
Mobile internet is expensive. Orange 30 day data bundles are BWP 9.5 for 10MB (or 7MB per USD), which is more than 10 times as expensive than in East Africa.
Settings: APN: internet.orange.co.bw, username: guest, password: guest

Namibia:
30 day data bundles are NAD 25 for 50MB (or 16MB per USD) from MTC.
Settings: APN: ppsinternet, username: <leave blank>, password: <leave blank>

South Africa
30 day data bundles are ZAR 49 for 50MB (or 16MB per USD) from Vodacom. Cell-C is cheaper, but less coverage outside of big cities.
Settings: APN: internet, username: guest, password: guest

__________________
http://www.movinghouse.ws

V useful post-
Made it into a sticky!

Also, if you are going to use a netbook or laptop with a mobile dongle and local SIM card, try to get it unlocked before you leave, or go in to almost any independant mobile phone shop/shack/kiosk in Africa, and they can usually get the dongle unlocked for you for a couple of quid - you can then use any SIM card on any network in Africa. Lots of people I met were buying a new dongle every time they travelled to a new country!
You will need to check the APN and password settings as per above post each time you use a different network provider.
(Tip - before you leave one country, find out what the APN and network settings are for the next provider in advance, as you won't be able to connect to the internet to find out without them...)

__________________
www.simba4x4.com

Swaziland:
Pay as you go from MTN is SZL 1 for 1MB (or 8MB per USD). 3G coverage is patchy. South African Vodacom refused to roam in Swaziland.

Settings: APN: mymtn.co.sz, username: <leave blank>, password: <leave blank>

__________________
http://www.movinghouse.ws

South Africa:

MTN have a data deal going - 187R (approx £14/$23) for 2 Gb - by far the cheapest I could find!

Dial : *99#
Username : MTN
Password : MTN

super-useful info
thanks