I don't think popular perception has caught up with the fact that urban crime in many many cities has gone way down. And if you limit "crime" to "crimes that are likely to happen to someone like me," where someone like me is someone who doesn't live in one of the worst neighborhoods and isn't personally involved in dubious endeavors, it's fallen even further.. My urban hellhole still has a lot of murders, though down from the peak, but I personally don't worry about being murdered.
I also feel quite a bit safer than I used to when I first moved here, despite moving to a "worse" neighborhood, and safer in many more parts of the city. I don't know how much of that is just a change in my perception, and how much of that is due to an apparent drop in muggings, etc..., but I really just don't worry at all.