When I lived in Manhattan (90-92) the worst thing that happened to me was that someone through a candy wrapper at me on the subway. Once.
Here are the rules I lived by:
1) walk with purpose
2) don't look people in the eye when walking
3) if you have to read a map (this was before mobiles) go into a building or store to do it
4) do not ask directions on the street
5) do not point at things
6) when on the subway do not look at anyone else and
7) do not touch the pole
8) if it is late at night, do not walk on the sidewalk, walk on the street near the cars away from dark doorways
9) do not wear or carry anything you don't mind parting with
10) I personally did not take the subway after 8 PM
11) I did not walk in the park alone during or after dusk
12) Now, I would not use a mobile on the street, I'd go into a building to call or look at data
Sorry if these seem blunt or over the top, but they are what kept me safe