Brazil has an exaggerated reputation for violence and crime. Yes, crime rates are higher than in the USA and Europe, but most of it is not directed at tourists. But - and this is the case everywhere you travel - , you are never immune from inconveniences. However, taking some common sense precautions can greatly reduce the risks of anything happening :

- dress down and don’t bring unnecessary valuables
- don’t keep your valuables together and don’t be obvious about what you carry of value
- make sure you know your way about before venturing off the main tourists areas.
And to reduce your mental stress if something does happen:
- take out a travel insurance
- make copies of important documents
- have numbers of consulates and credit card companies ready to call

Links:
http://en.brazilny.org/index.php?/consulado/tourism/safety_and_security http://www.braziltravelvacation.com/brazil-safety.html
http://www.ez-riorentals.com/tourist-info.htm#issues