Wear a money belt inside your shirt or pants for your passport, credit cards, and any other valuables. Leave the wallet at home. I only carry one day's money in my front pocket to minimize my loss if robbed by pickpockets, according to Rick's suggestion. We try not to use Bancomats, ATM's, near popular tourist spots to reduce the chances of attracting thieves. A few years ago we were leaving the Vatican and stopped at a Bancomat on our way to the Ottiviano Metro stop. Three kids around 10-12 years old must have been watching the location and followed us into the metro stop and attempted to pick my pocket. They were fast, but unsuccessful and left with nothing. One ran in front of me and stopped as were were entering the railcar, the second one bumped into me, and the third tried to pick my pocket. This is referred to as the stall, the bump, and the dip.
My wife is 71 and I'm 69 and have noticed we attract more attention from thieves because we are older. When we are with my family or in a smaller town I do not use a money belt. I look like I belong in Italy, but my clothing gives me away. I have a small leather business card case, which I use for my credit cards, driver's license, and ATM card.
Go and have fun, but be aware of your surroundings.
Buon viaggio,