My boss just got back from a business trip to Hanoi. He was taking an Uber to the airport to return home and got into an accident. The driver was going way too fast and playing with his phone, even after my boss (a pretty polite person overall) asked him many times to watch the road. They rammed into a truck that had the right of way, and if my boss was in the passenger seat instead of the back seat, he would have been severely injured. (The pictures he took were really scary.)
As it stands, he flew home to Korea with a sprained wrist and was very shaken up about the the whole thing. The Uber driver literally refused to call for the police or an ambulance for fear of getting arrested, and as mentioned, if this had been a more dangerous accident, my boss would have bled to death by the side of the road.
I'll admit, I've opposed Uber from the beginning because of their unfair labor practices. They are the definition of "Vulture Capitalism," not building something new, but just exploiting inefficiencies to make a buck and then move on. But I'd also suggest that in underdeveloped countries you are taking your life into your own hands in an Uber. Sure, a regular cab driver might behave the same way, but at least you could contact a cab company. Hopefully, you'd have a more experienced driver to start with as well.
As it is, Uber drivers are basically internet-contracted Gypsy Cabs, and I would never take a Gypsy Cab in New York or anywhere else.