We prefer small belt packs for convenience and safety. They used to mark you as a tourist, but not any more. Avoid dense crowds and don't be distracted. This the best picture I could get of the Mona Lisa which illustrates the kinds of crowds you can encounter on vacation. It doesn't take a crowd, either.
Thieves are artists at distracting tourists so they let down their guard for that important second.
On a TV program on this subject they showed two thieves working together. The second person grabbed the purse and ran. Studying a map is a sign of a tourist. Try to do it in your hotel room or at a restaurant table. I admit I don't follow this advice except when I'm a little nervous about the district I've found myself in.