Tough call; you certainly have to be aware of the risks and actively take counter-measures. This also applies in South Africa. For example, when driving in certain parts of ZA (places like Hillbrow in JNB) you must not stop at a red light; and the traffic laws actually permit you to run red lights under these conditions. This has gone on for a decade; but single white women tourists are specifically targeted (as they are unlikely to be carrying a gun or to come back and testify at a trial). South Africa is one of the few countries in the world where more people die from shooting as part of commission of a crime than from car accidents (and after you see the driving conditions, that statistic becomes even more amazing).

There are approx. 25,000 murders a year, and about 90% of the victims are male. My own feeling is that South Africa can be very safe, if you are savvy and pay attnetion, but there are situations that are 100x more dangerous than you would find in the US and it isn't difficult to blunder into some of those situations. Remember that some people make a dollar a day there, the depth of poverty and desperation can be quite significant. In most ways it is much worse in Zim, though the police there watch out for the tourists as the regime is desperate for the tourist dollars.