I thought I'd share a story. A good friend of ours has been to Rome numerous times. I think it's widely acknowledged that there is a pickpocket problem. He saw a lady walk up to a man and toss her infant to him. Of course, he did everything he could to catch the infant. While he was catching the baby and his hands were full, children were pickpocketing him.
I've heard from more than a few people that the key is to not make eye contact with people walking towards you, near you, or approaching you in any way. If you do, turn quickly and walk away. Anyone coming up to you randomly is doing so just to distract you.
BTW...We're taking cross packs, sister is taking a purse/backpack, and we've talked about using a twist tie or something like that (wire) to twist the zippers closed or together.
When we were in Milan, Florence, and Venice, we felt very safe, and never had a problem. While in crowded places, we did take precautions such as putting the crosspack, purse, bag, whatever; in front of my body with my hand on it. Sometimes I would even place the bag between my body and my husbands depending on where he was standing.
I think sometmes people get wow'd by the sites and forget to be careful about their "goodies".