Crime was on its way down long before Mayor Bloomberg, and for that matter Mayor Guliani caem on the scene. Factors are many, but much of it has to do with LE methods, changing demographics, and the nature of "crime".
Much of what drove crime, illicit drugs and prositution amoung other things are still around, and probably in greater numbers; however the Internet, cell phones and the like have made standing around on corners obsolete. Saying goes you can order ANYTHING to be delivered in NYC, and that is very true.
Still,while it is safe to walk around most if not all parts of NYC, especially at night; one simply must use some common sense.
L.