Travel to Brazil can be safe so long as travelers use a bit of common sense and discretion on their trip.
For some travelers the issue of a safe trip never (ever, ever) crosses their mind. But, if you're heading to the country of Brazil; it is best to make sure you're on your game.
No, I'm not saying that Brazil is some crime-ridden country. Far be it from me to ever suggest such a thing--I'm only saying that as long as you don't leave your common sense back home, you'll be all right.
Rule #1: Don't drink too much. Sure, it's quite easy to get swept up into the circus of Carnival--but if you've imbibed a little (a lot) then there goes that common sense right off the side of the parade float.
Remember, if you're sober--you'll have more control over your belongings.
Rule #2: Avoid public trams and buses, if you can. Crowded public transportation can be a smorgasboard for pickpockets. Spend a few extra bucks for prepaid taxi tickets. When lounging around Brazil's beaches, remember not to leave your camera/keys/money unattended; not even for minute as petty theft is quite rampant.
Rule #3: Women travelers would be best served by taking taxis, and not really walking around after dark alone. While violent crimes against women travelers aren't very common, date-rape drugs have been known to be used to incapacitate victims to steal their money.
And whatever you do (this goes for men, too) try to avoid venturing "off the beaten path", or visiting Brazil's famous favelas. But, if you're going to--make sure you've gotten yourself a proven trustworthy guide.
Rule #4: Keep your cash off your person. Carry only the minimum you need, but also be wary of ATM fraud. While not all that common, kidnappings have occured around the money machines with traverlers being held for "ransom", only to be released after clearing out their bank accounts.
Rule #5: Food safety. Brazil isn't a Third-world nation, but it is best to know not to drink local tap water (it is OK to use to brush your teeth/shower)--stick to bottled water for drinking (and don't order ice for your drinks). Also, try to avoid eating seafood from beachside vendors, undercooked meat, and no raw fish.
Rule #6: Get up on your vaccinations. Talk to your doctor before you leave about protecting yourself from Yellow Fever, Malaria, and Dengue Fever--especially if you're gonna be out in the jungle of the Amazon.
Rule #7: The United States State Department (or whatever country you're coming from) can't really help you if you're helping to smuggle in illicit goods in or out of bordering countries like Argentina, Paraguay, or Bolivia. The Brazilian/Columbian border is more commonly known for kidnappings and drugs. Be very vigilant if you're in this region of Brazil.
I know it sounds like Brazil isn't a very safe country to visit--but again, with some common sense and an attention to your surroundings you'll have one of the best adventures of your lifetime.
Now, with all that out of the way--what are some of the best places to vacation in Brazil?
Bahia in general - this is a northern state.
Rio De Janiero