Sicily travel faqs and travel safety pages but we'll present it here:
If you're walking down the street, walk on the side toward (facing) oncoming traffic. On the sidewalk (on newer streets), walk toward the flow of traffic but not right next to the street, leaving some space between yourself and the cars and motorbikes. Hold your purse on the side away from the traffic.
Increasingly, purse snatchers work on foot (usually in pairs) rather than on motor scooters, especially during the day. The thieves generally prefer narrow, winding streets. Don't explore the older sections of larger cities (Palermo, Catania) alone if you can avoid it. While the thieves are less likely to try to snatch a backpack you're wearing, hand bags are tempting. Don't carry one at all if you don't have too; keep your money, credit cards and travel documents in pockets. Don't wear gold or pearl necklaces, which might also entice thieves to assault you for the jewelry. Better yet, don't wear any necklace or bracelet. Most assaults are directed toward women. Having one or two men with you is not a bad idea. People in tours of Sicily (groups of six or more) are rarely targeted.