If you plan on taking the commuter train that makes many stops along the way from the airport into Rome, beware of scammers who prey on weary travelers who are fresh off the plane and disoriented. Watch your stuff, keep them wrapped around you at all times. They work in groups of 4-5 (or more), one will scout then notify his cohorts, several to distract you, one to nab the stuff. Don't sit near train doors, if you think it's easy for you to get on/off, it's easy for them to get on/off too. They know the timing of when the doors will open and close. They are not limited to just one distraction (e.g. bumbling fool dropping his coins), but they have backup tricks if the first one didn't work. Keep your hands on your stuff, wrapped around them.
If you lose your stuff, file a police report right away, note the location that you think it happened at. (And no, the police are not going to do anything about it other than to take the report and give you a copy). Keep a hard copy of your passport with you (separate from your passport of course) in case you lose your passport. Subway stations have photo booths that takes your picture for 5 euro. To replace your passport, have the hard copy, new photo (or if you brought one with you that's taken w/in the last 6 months), and the police report, it'll make life a lot easier.