European, australian, american nationals are exempt from visa requirements for Botswana and Namibia. In order to visit Zambia or Zimbabwe it is necessary to obtain a visa, which is available on the spot at the border posts, and payable in US dollars.

Please note that your passport needs to be valid for more than 6 months after the date of your return and needs to have at least two blank pages in it.
Should you travel with your family, please check the requirements for children in South Africa (even for a transit) and in Botswana.