Have used Uber all over the U.S. (but mostly at home in the Bay Area) and in Amsterdam and Lima.

In Lima about half the time the cars were the sketchy unofficial taxis, but I felt safer knowing Uber was tracking the ride, and other than the typical hectic driving I didn't feel unsafe during the ride(s). Once a driver seemed particularly insistent about something (that I approve his route?) before we left, but the language barrier got in the way (Spanish is not one of my languages, unfortunately!) and it was fine in the end. Still would be interested to know exactly what he was concerned about - tried to explain to a local tour guide later, but she had no clue either!