The income disparity in Rio is great and when you are packed into a tight place like Copacabana, where wealthy tourists rub shoulders with poor locals, things are bound to happen. That being said, I was in Rio for about five days without any major incidents: a kid who wanted my watch (who I just waved away) and some locals calling us names. There are areas that are more prone to crime - Copa and Downtown, where it is really crowded. I found Ipanema quite safe. Don't carry lots of cash, wear modest clothes and no jewelry, don't wave your cameras around, stay away from the beach after sunset, and don't walk to your hotel drunk at night. Sounds like a long list, but is probably applicable to any large urban area. Rio is a beautiful city and the people generally are very welcoming - don't miss an opportunity to see it (although I am glad I went before seeing "City of God").