There are questions on the safety of travel in South America. I have therefore summarized in this page my personal experience from more than 3 months of independent travel in South America in 1996.
We encountered two pickpockets during our journey. The first situation occurred in Rio de Janeiro in a city bus going from Copacabana to the city center. A group of two or three people worked together. One blocked our way in a narrow passage and the others were examining our pockets and backpacks from behind. They were not agressive and tried to be inconspicuous. As we had nothing in the upper pockets, they were unsuccessful. The second pickpocket was trying to take something from the pocket of my friend on a street in Arequipa, Peru. The result was the same. Another not so clear situation occurred in Bolivia, in the Chacaltaya hut near La Paz, when one man of the staff was looking into the bag of my friend, when the bag was abandoned for a while.
We encountered no problems in the hotels, even if we often used to store a part of the baggage for few days in hotel deposit, when going to a trip. We also encountered no problems in long distance buses, even when travelling during night (in Peru we travelled the routes Puno-Cuzco-Arequipa and Huaraz-Trujillo-Tumbes at night, in Colombia the route Cali-Bogota).
In summary, the situation in South America seems to be not so bad. We met many travellers, even single women, who had no severe problems. Of course, there are reports of severe attacks from time to time, so nothing can be excluded. Two friends of mine were robbed in Venezuela, the country which we did not visited.