There's no need to be frightened--just careful, as you might want to be in Rome, Madrid, or other big tourist attractions. We stayed in Copa, right on the border of Ipanema/Arpoador, went to the beaches in the day, walked the oceanfront avenue in Copa and many streets in Ipanema in the evening. We were far from any favela and near to crowds of people, many of whom warned us to take care of cameras and shoulder bags--like we would in lots of places.

It would be a big shame for someone to avoid Rio or the beaches there because of fear of crime. Keep your valuables locked up, stay where there are people, and enjoy.