Italy suffers from racial stereotyping as much as most, and the ‘Goodfellas’ image perpetuated by Hollywood bears a large part of the blame. There is organised crime in Italy, from the Sicilian Mafia and Neapolitan Camorra, to high-level corporate crime. What violent crime there is tends to be domestic, rather than directed at tourists. Italy is a safe place to be, though in the big cities pick-pocketing has been developed into a fine art.
Theft from parked cars and purse snatching can also be a problem in large cities. Predictably, most thefts occur at crowded tourist sites on public transport, or at the major rail stations, where many people are invariably confused and distracted.
While in any foreign country you should act cautiously and remember to switch on your commonsense detector. In preparation for your time abroad you should make a list of the emergency numbers for your bank, credit card issuer and so forth. Also take photocopies of your passports and financial documents, and only carry the cash you need when out and about.