Laura, I have never had a safety issue in my entire 12 years living overseas. (My car was broken into once in Mexico, but that had nothing to do with personal safety.) I used to be able to say that I never knew a single expat who had experienced a safety issue, but of course after 12 years that’s not true any more. (and not just Ecuador… I think crime is rising around the world, even in the US)
I don’t, though, feel at all unsafe in Ecuador and I will take a bus or a taxi by myself just about anywhere. I find the locals to be helpful and concerned. I have always had great experiences with taxi drivers. In larger cities you may find some instances of purse and phone/camera grabbing. You need to exercise caution and be aware of your surroundings.
What we don’t have in Ecuador is much violent crime and/or gun crime. (Guns are hard to get.) No random school or mall shootings. I know that the occasional home invasion happens, but but it is rare to hear of them (I can only think of two against expats that I’ve heard of in the last five years)… and again, in Ecuador you should take responsibility for your personal safety. You can’t count on calling police and having them respond in a matter of minutes. That doesn’t happen here. (One reason our property taxes are so low, I suspect.) That’s why all the locals have bars and windows on their homes and security entrances to condo buildings. The more you do to protect yourself, the better off you will be.
That said, I have never had a safety issue in 12 years in Ecuador. Do note, though, that I live in a very small, safe town.