Pickpockets and cons.
As with any major city especially those attract a lot of tourists there are people who are out to steal from you. It is no different in Rome but with a little planning you will make it difficult for these people and also if you do fall prey you will only lose a little. We will start off when you arrive, there are always people waiting for the chance to steal a bag from you, especially around the main Termini station. Ensure you keep hold of your bags at all times, if you need to buy a ticket then keep your bags in front of you at the counter.
Next to be wary of is pickpockets, start out by leaving anything you do not need in the safe where you are accommodated including excess money, credit cards and passports. You are supposed to carry identification in Italy so carry a photocopy of the photo page in your passport, I would rather be in a little trouble for not carry I.D. than going through trying to replace my passport overseas. Do not take a purse or wallet as that is what is normally targeted. A money belt is good but a bum bag is not so good. If you put money or credit cards in a bag then try and use an inner zipped pocket. If you have trousers spread your money around pockets, horizontal openings in pockets like in jeans are good, vertical openings such as in slacks are not so.
If anybody comes up to you and starts speaking in English straight away always be wary, if they offer you something for free as a thank you for your help, just walk away as there will be a catch.