NY is very dangerous
Before I went to NY several of my family members and friends warned me about NY.
They told me to watch out for purse snatchers, burglars, stabbers, and so many other things that they thought I would come across. They basically said that NY is very dangerous.
However, when I was in NY. I felt pretty safe. There are cops all over the city and nobody tried to steal or stab me.
Some people freaked me out by praying very loudly during one of my subway-riding days, but either than that I felt as safe as being back home.
I think that NYC is pretty safe and gets a bad name because of its past. People should realize it's not like that anymore.

Research:
Since everybody kept telling me that NYC is dangerous I thought I would find it for sure on the top of Forbes' most dangerous cities in the US list.
I clicked and clicked on the 2011 list and I couldn't find NYC anywhere.
Instead, I found NYC on Forbes' 2010 safest cities list! It's the number 6 on Forbes' most safest list.

Source:
http://www.forbes.com/pictures/efel45mde/7-stockton-calif/#gallerycontent
http://www.forbes.com/2010/10/11/safest-cities-america-crime-accidents-lifestyle-real-estate-danger_slide_6.html
http://www.forbes.com/sites/johngiuffo/2011/10/03/americas-most-dangerous-cities/