Rome is not a dangerous city but pickpockets and bag-snatchers are active. Wear a money belt under your clothing and wear your bag across your body. Beware if someone knocks your side mirror as they may snatch your watch as you reach to fix it. Watch out for groups of dishevelled-looking women and children carrying bits of cardboard which they use to distract you while they swarm around and pickpocket with lightning speed. If you are being targeted by a group, either cross the street, or shout 'Va via!' ('Go away!') in a loud, angry voice. Be careful on crowded buses (the No 64 bus, which runs from Stazione Termini to the Vatican, is notorious), the Metro (head for the end carriages, which are less crowded) and busy market areas. There is only one foolproof way to deter pickpockets: simply do not carry any money or valuables in your pockets and be very careful about your bags, even in hotels.
Parked cars, particularly with foreign number plates or rental company stickers, are also prime targets for thieves. Try removing or covering the stickers, leave a local newspaper on the seat to make it look like a local car and opt for supervised car parks.
Beware of dodgy shopkeepers short-changing you. Acquaint yourself with euro denominations and count your change carefully.