South Africa is a very popular tourist destination and most people visit the country with no problems. However, it is also known for its high crime rate, so travellers are advised to be careful.
It is not advisable just to set off from your hotel, apartment etc and explore. Wherever you are staying, you should ask advice about the best areas to visit and which ones to avoid. If there is an option of joining an official excursion or guided tour, this may be a good option to consider. If you do go off alone (not recommended) or in small groups, it is best not to wear expensive looking clothes or jewellery, to take out money openly or to be seen with expensive accessories like mobile phones.
If you drive, be careful about stopping at lights, always be alert and keep the doors locked. Don't leave anything lying on the seats. Also be careful about hiring a taxi or other transport - it's best to stick to firms or drivers recommended by your travel agent or similar.
You can find some more safety tips here.