This question is actually more appropriate that it seems since countries like France give a strong advice against visiting countries like Colombia or Peru, both countries where I have actually been. Ok I have never had any problems but I have also tried to avoid having problems as much as possible. Basic ideas you come with when you first travel there are: do not go to slums or dodgy areas, do not show around that you have a 1000$ DSLR or a rolex or whatever else that costs money, do not leave your bag to someone you don't know, etc.
But there is things that you might not have think of and that's where you actually realize that if you are a bit unlucky and uncautious it is possible to have problems that can turn in very bad situations sometimes.
For instance, I have met in Trujillo, Peru an american guy accompanied with a local women that came to me asking if i could understand both Spanish and English. I said yes, and she started to ask me in Spanish if I could ask the guy in english if everything was ok and if he needed anything else. Ok the guy looked a bit sketchy but most backpackers like I also do so I wasn't expecting to hear what he told me.
image: Policemen in Lima, Peru
He woke up at 5am, took a cab to go from his hostel to the center, and suddenly the cab driver started to act weird. First stopped at a gas station, then started to drive around some blocks while talking on the phone, and finally stopped the car in front of a group of guys. 4 guys pulled him out by force and started to beat him up to get his money. Apparently someone had even biten in his arm as he was trying to stay inside the car while giving kicks whith his legs. In the end he had his camera stolen, they torn appart his jacket to get his wallet with all his money, credit card, and everything else. And the poor guy had only something like $50c to go back to another place where luckily he had left his backpack with some money and his passport. When you hear that, the first thing you think of is "shit that could have happened to me too", even before thinking "poor guy".
The more you travel, the more you hear of similar stories. 2 guys in Quito, Ecuador that got "assaulted" with mustard and ketchup and while one guy was insisting to help them clean the mess, the other one stole things in their backpacks. Even better, someone in Guayaquil, Ecuador that simply got asked by a taxi driver to give away his wallet and all his money. The taxi driver was pointing a gun at him.. And still even "better", a french women working for a NGO that one night got shot down in Quito for something like 20$, that had to wait 2hours in the hospital before getting surgery since she didn't have her credit card with her, and that in the end didn't make it...
I would say that in all countries I have been to and not only Ecuador there is some places that are unsafe. Though Quito and Guayaquil became recently notoriously famous for being unsafe I wouldn't say that Bogota, Cali, or Medellin in Colombia nor Lima in Peru, nor La Paz in Bolivia are safer. In general, it is better to pay attention in capital cities where crime is more of a problem that in small cities or in the countryside where I have never felt unsafe nor heard any stories.
Therefore general safety rules are: always try to take an official taxi, do not hang out by yourself after 10-11pm and until 6-7am, always pay attention to your backpack in bus stations or in minibuses, always pay attention to your wallet and camera when you take public transportation which are always crowded and full of pickpockets.
In the end there is many places that you would miss if you're simply scared of going there because you've heard or read stories about it. Simply know that locals know the best about what to do, where to go and not to go. Most of them will actually tell you that during the day it is safe almost everywhere and especially in the center with the presence of the police. So the best advice I can give is just to go ask local people, and you might also end up having someone showing you around the city, inviting you for a drink, or simply telling you about a place that is not written in any tourist guide :)
image right: policemen in La Paz, Bolivia
image left: policeman in Cuzco, Peru
