I know this is a very late answer to the question, but would like to add to what was said so far for future readers interested.
Visible crimes that are very common in South Africa are rapes, car jackings, house and business robberies often leading to murder of the victims, farm murders, and "gang related" crimes like territorial conflicts, drug abuse etc. With this said, this is the typical crimes the residents are faced with, that tourists might not encounter at all. When you watch the news of things happening in other countries, it's almost the same, and I almost become scared of thinking to travel to those countries, and would rather just stay here and face the problems we have here. This is a wonderful country, and basic survival instinct will keep you safe.
South Africa can be considered a dangerous place because of a few things:
Poverty and unequal distribution of wealth: Where there's poverty,
there's crime, that's a fact everywhere around the world, and also
because of the political history of the country, most of the wealth
is still possessed by a minority of the population (all races
included). The impoverished majority might feel that the wealthy owe
the poor, or that the wealthy don't really deserve their wealth.
Corruption: Organized crime is a reality, and government officials are either complacent about the fact, part of the criminal
organization, or has close friends or family members in criminal
circles which they want to protect. This flows from the highest
level of government all the way down.
Remnants of the political history. The masses have very little education with respect to the history of this country, and rely on
the stories told to them by their parents and grand parents. This
leads to subjective perceptions which is not in line with actual
facts and statistics. This breeds hatred in the hearts of those
masses, which may or may not overflow into criminal activities
against those perceived as the enemy.
This website gives an interesting view of the dangerous parts of South Africa.