I've found this useful advisory tips from the website of
Traveling with Ed and Julie
I am from Rome and I can confirm that these guys they know what they are talking about...
"Crowds are fertile territory for pickpockets anywhere, and Rome can be crowded, especially on the bus or subway. Beggars (often characterized as 'Gypsies') are a problem. We'd give a wide berth and take a confident stride away from any urchins beseeching you for money - the only donation they want is your wallet.
Teenaged girls surround an individual, perhaps with the addition of cardboard 'shields', grab a purse or camera bag and run.
Motorscooters can be used to ride next to the curb and grab purses and bags. (Should this happen, let it go - don't be knocked down and dragged into traffic.)
These are the things to look out for in anything remotely a crowd:
Pickpockets. Never carry more valuables on your person than you can afford to lose. Ed does carry money, cards, and passport in a shoulder holster under his shirt. He keeps his hands in his pockets where he's got a small amount of money, and pays attention to the straps on the camera bag, rarely carried. There are versions to go around the neck or hang from a bra, and some still like moneybelts.
Groups of teenagers, especially (it seems) young girls. If a group approaches you, avoidance is best: shouting will chase away most; kicks will deter the most-determined.
Distractions - especially the Gypsies and their kids. (Apologies for what may be a politically incorrect stereotype -- surely most Gypsies are hardworking and honest.)
Regretfully, our experience says raise a red flag when you see what look like Gypsies, whether they're really Gypsies, or others in disguise -- particularly when they're accompanied by youngsters from the age of two weeks up. They're usually easily walked away from and ignored. They're aggressive, but too busy to bother with someone who doesn't want to be an easy mark.
Scooters - keep purses and camera bags on the building side, and away from the curb.
Avoid looking like an easy mark - look like you know where you're going.
Fanny packs (bum packs, if you're British) are an invitation to theft.
As far as shoulder bags and belt packs are concerned (as well as purses): Assume anything you have over your shoulder or on your back can and will be opened, cut open, cut off, torn off, etc. (Cynical, aren't I? Rarely happens, but it does ... at home and abroad.) Keep as little of value in places other people can get to as possible, and keep most of your money, credit cards and id securely tucked away out of harm's reach.
When sitting at a table, or on a seat on the subway or bus, for example, don't put your bag down on the ground behind you unattended. Hold it in your lap if possible. If not, loop the strap around your chair leg, or your chair.
The areas in which you should particularly be alert: restaurants, cafes, bars etc.; airports, train, subway and bus stations; heavy tourist areas; the area generally around the Capitoline Hill and Roman Forum and running down toward the Colosseum are particular favorites (and don't forget the Termini Station and the bus 62, 64).
In general, and we admit to finding this irksome and easy to forget while on vacation, be alert. Enjoy the sights, and don't, for goodness sake, be paranoid. Do be aware of what's going on about you, and who's there.
Frankly all of these (except maybe the unique Gypsies and the excess of immigrants) are concerns in any large city. The steps you can take ought to be taken in any urban setting.
We're convinced Rome is no less safe than most large cities, and certainly safer than many American cities. As well, there is far less violent crime than in American cities.
We, personally, would never stay away from Rome because of the petty crimes, but alertness is called for more than ever. By staying alert, you'll have the opportunity to skirt obvious opportunity for mischief.
Remember: your vacation day is a thief's workday. Assume a parked car will be broken into. Assume a group of youngsters are up to no good. Be alert, and don't look like a lost soul.
Finally, while petty crime is common, violence, knives, and particularly guns, are rare. Most tales are exaggerated, but do take the precautions you should in any other urban situation.