Let me start out by saying that in my year being in Brazil, I have never run into safety issues or been in bad situations. This includes during the first few months where I would walk everywhere by myself, even at night – which I later learned was NOT recommended.
This applies to most Brazilian cities, especially the big ones like Rio de Janeiro, Sao Paulo, and Salvador. In fact, the locals are often the most paranoid ones: hiding their car radios, driving two blocks in Liberdade to avoid walking (to me this is excessive as we could not find parking and had to walk two blocks anyway :p)… I know people who have been mugged, although no physical harm was done to them. Who am I to argue with the locals, so eventually I became kind of paranoid too. Things are OK during the day, but at night, please take a taxi!!
It is safe to hail a taxi on the street, but the Brazilians in-the-know use a taxi calling app, called Easy Taxi.
It is an international company and it has great coverage in Brazil. You can find a list of the Brazilian cities they are in in Brazil, 34 at the moment, which includes almost all the major cities. No Florianopolis, unsurprisingly… in Florianopolis it is best to google for taxi in the neighborhood you are in, or ask the hotel or hostel to call you a cab.
Easy Taxi uses GPS and is a great way to call for a cab in the comfort of your home or hotel, and it tells you when your taxi will be arriving, just like Uber. I love that when the taxi arrives, it announces the arrival with a singing “taxi! taxi!” voice. An added perk is that if you lose something on the taxi, it is a great way to get it back! You can pay with cash or credit card. You can often find promotional discounts, for example the code etaxi2015 will give you a $R15 discount until the end of January 2015 (you have to choose to pay by credit card). Their facebook page is a good source for discounts.