While you're unlikely to be a victim of violent crime in Italy, when traveling in tourist areas in big cities like Rome and Florence you may be a target for pickpockets or purse snatchers.
To avoid loss, it's always wise to carry any important documents (like your passport), your credit cards, and most of your money in a travel security wallet or passport holder that can be worn under your clothing. While it may be slightly uncomfortable, you are much less likely to loose anything of value. I usually carry a small amount of cash and one credit card in my purse, pocket, or pack where I can get it easily and the rest is stashed safely below my clothing.
If you're traveling with another person, divide your credit cards so you're not both carrying the same ones. If one person's wallet gets stolen you'll still have cards you can use.
Before you leave for Italy, be sure to write down the foreign phone number for each ATM and credit card for reporting lost or stolen cards and make a photocopy of all your cards to keep separately. Make a photocopy of your passport, too. Keep these separate from your originals.
Remember, use the same common sense you would use in a big city anywhere in the world. In crowds, such as on Rome's metro, it's better to carry your pack or purse in front of you where you can easily see it. Always be aware of your surroundings and don't put your purse, day pack, or camera where someone could snatch it. If you have zippers on your purse or pack, be sure they're closed.
Be wary of people asking you for money or asking you to do something for them. In Rome, tourists are sometimes approached by someone holding a piece of cardboard in front of you for you to read. While creating this diversion, a child or another person, picks your pocket.
Taking these precautions could save you time and trouble. Here are examples of travel security items from other about.com travel sites: