If you figure out where to live by the crime rate, many of the safest places to live are outside the United States, where crime, though lower than it used to be, is still high by Western standards. Here in Israel, for example, fewer than 200 people are murdered a year. In the U.S., about 17,000 people were murdered. Of course, these figures are not comparable due to the fact that Israel has around 6 million people as compared to the U.S.'s 300 million.
Crime rates and murder rates are typically adjusted for population by reporting the number of crimes per 100,000 people. In Israel this rate (for murders) is about 3, as compared to about 6 per 100,000 in the U.S. Even including terror attacks, the rate has never been as high in Israel as in the U.S. In England, the rate is less than 2 per 100,000, which is in line with most of Western Europe.
All this is fine and good if you are willing to live abroad just to enjoy a lower crime rate, but, assuming you are looking for a nice place in the US to live, what city might suit your needs vis-a-vis lack of crime?
I considered the four cities I have lived in (see the FBI site for all the stats), Columbia, SC; Washington, DC; Phildalephia; and New York. Of these, New York (sorry Mom) is clearly the safest, with a murder rate of 6 per 100,000 and a violent crime rate of about 0.7% (less than 1 in 100). The worst is DC (murder: 29, violent crime 1.5%), but Philadelphia is a near tie (26, 1.5%). Columbia, my home town and my parents' current and future town, is in the middle (13 murders per 100,000 and 1.1% violent crime rate).
These stark differences mask three important facts. First, the chances of a random individual being a victim of a violent crime in any given year, is very low, no matter what the city (though it's more likey to get killed by a person than a car in Philly and DC, according to National Safety Council statistics--originally linked here but apparently not on the web anymore as of at least 11/28/2012).
Second, most violent crimes are committed by someone we know, and most of the people reading this blog do not have violent acquaintances, plus most murders are committed with guns, and most people reading this blog do not have acquaintances with guns.
Third, crime is highly localized, and no matter which city we live in, we are likely to live in a more affluent area, and these areas have much lower crime.
So, in conclusion: don't worry, Mom, New York is safer than Columbia, as long as I can keep making a living!