I got mugged at knifepoint in Cape Town - the 'safer' alternative to Joburg. I think if you go to South Africa you have to accept that the there is a massive crime problem and alter your mentality from the (thankfully) laid-back Australian way of living.
As described by others:
1. Airports can be pretty dodgy. Arrange a transfer to meet you if possible, either from the hotel or they should be able to arrange a reputable person who they use for transfers. I stayed in a hostel (was a student when there) and they had this option in place, so nicer places should definitely have this. The taxi drivers/porters/touts can be a problem, and in some cases dangerous.
2. Whilst Cape Town is 'safer' than JoBurg, it is by no means safe by Australian standards. In middle class neighbourhoods, it is not uncommon to see houses with fences, gates, security systems and sometimes a guard. In our dubious student share house we had a massive fence topped with barbed wire, and two deadlocks on the front door.
3. Take reasonable precautions (don't look like a tourist, hide the valuables etc)
Then take unreasonable precautions.
As an example, using an ATM:
Don't carry your wallet on you unless absolutely necessary. Carry cash for the day, and one or two cards if you expect to need them. Find ATM with decent lighting in a public location (shopping centres/supermarkets were quite good). Examine surroundings carefully. If someone loitering, standing too close, otherwise worrying you, walk away. Approach ATM, look for signs of tampering. If so, walk away. If not, put your card in. Immedicately cancel the transaction to ensure your card is not going to be retained - there had been a lot of ATM tampering where your card got retained by the machine and either someone watched you or a video taped you entering your PIN so money could be stolen, so always make sure your card is returning to you BEFORE inputting PIN. Before reinserting card, paranoid look at surroundings again. Ensure noone can see PIN, including no mirrors atop the machine. If all happy, get dosh, stash somewhere safe, look around you, walk away...
If planning on driving, there are certain areas that are no-go zones - the townships in CapeTown, especially Khayelitsha. There are also areas where you don't stop for red lights after dark due to carjackings and thefts. Your hotel can help with this. Also, when parking the car there are young men who make a living "guarding" cars - you park and find a young black man who will guard your car in return for a few rand. Frequently this is not an optional extra.... if the money isn't paid your car or pieces of it may not be there when you come back! I'm not sure if this is still occurring, but was common at the beaches and other tourist areas at the time (2006).
All that said, South Africa is a beautiful country and I enjoyed my time there. The Cape of Good Hope, Simon's Town, Table Mountain and Stellenbosch winery region were all well work visiting. I would suggest the more local knowledge the better - if you have friends, colleagues, couchsurfers who live there or used to live there, then tap their knowledge.