I used to live in southern Italy. There were definitely pickpockets (and other varieties of thieves) around, but I was never 'taken' ...

Keep your wits about you - pay attention to people walking up to you and/or following you. Keep your wallet in your front pocket and/or leave the purse at home.

I think I got away because I also walk very fast. Maybe I'm a hard target because - once someone notices me as an American, they'd have to run to catch back up to me and thus risk drawing attention.