If you are traveling to Rio you should be concerned about crime but not so much as to change your travel plans on coming down here.
I´m an American living here in Rio and I´ve seen lots of thing happen here, really bad things but as a tourist you should stick to the tourist areas but be aware that the people there are there to scam and sometime prey on tourist so you should always be aware of your surroundings and stay out of the Favela (Brazilian ghettos).
This city is too beautiful to not visit. Stay alert and you´ll have a great time.
Trust me. I came here for two weeks in 2001 and havent left yet.

Lost in Brazil