Children are just as safe, if not more so than they were years ago. Bad things have always happened that have jeopardized the lives of citizens, the difference now is that we have 24-hour news access due to the Internet and television which forces us to notice all of the bad things going on in the world. Bad things have always happened, we just weren't always aware of them in the past.
No, our children are not safe anywhere, because there is always something bad that can happen. A child can trip and fall down walking down the sidewalk. There will always be a person that is capable of harming them. We cannot put our children in rubber rooms and protect them from everything.
To make a long story short, no, your children are not safe. No one is guaranteed 100% safety, regardless of where you live. Safety is far more abundant in the United States than it is elsewhere. This is mainly because we rarely have riots, or fight wars on our own turf.
I would argue that no one is perfectly safe anywhere. The chances of a car driving through a day care are very, very slim. Children get hurt in their homes all the time even with parental supervision. Life is always risky no matter how old a person is. The world has become a lot more safe in the last 50 years.