Always watch your baggage and cameras. If you put them down, put a foot through the carrying strap. Keep your camera in front of you. Watch one another. Don't allow yourself to be distracted by any strange events.
Violence is most unusual.
Most South Americans are great people, humourous, generous and cheerful, in spite of the extreme poverty some have to endure. There are some quite nasty diseases, read the Lonely Planet guide carefully. In the poorer countries I have found food hygiene to be the worst problem leading to diahorea. However there's no need to be paranoid, the chances of anything serious happening to you are remote. Good travel insurance is a must.