Quito is not dangerous for a Latin American city, especially if you take precautions.
For example, make sure you only take official taxis with a (partly) orange license plate and a registration number on the side.
After dark, it is better to not walk through quiet streets.
In buses and busy spaces, like sports events, you have to be careful of pickpockets.
Earthquakes are also pretty common in Ecuador and although most of them are minor, make sure your house or apartment is built according the current construction laws.