Everything I've read, both on the internet and in travel guides, says that pickpockets ARE a big problem. Naples is supposed to be the absolute worst place.
I think we'd all be smart to buy/use one of those "pouches" that go around your neck and under your clothing for money and important items while touring the cities.
In some of the travel catalogs (like TravelSmith and Magellen's) they have purses and camera straps that actually have wire in the straps. I guess some of the pickpockets just take a razor blade or knife and slash straps. I've also heard of them slicing the bottoms off women's purses.
So, I think we should be extremely careful. I plan on using a "pouch" for money and will carry nothing but lipstick, tissues (Lots of tissues since TP is reported to be in short supply!) and maybe a bottle of water ...nothing important at all.