Well, as a friend of mine who is the son of a cop always said, "opportunity enables crime." Interpret that how you want.
When I travel abroad I stay discreet and don't carry anything flashy. I may feel 'blah' without certain jewelry, shoes or bags but I know I'm probably going to stand out as a tourist no matter how hard I try to blend in and the more non-descript the better.
Yes, when going into rougher neighborhoods I do stick with more nondescript things too and always, no matter where I am, project a confidence when I walk down the street, even if I am lost and have no idea where I am. Works like a charm.