Anywhere that tourists congregate, although the Spanish Steps seem to be a hot spot, because people tend to sit and put their bags down and often don't keep a close eye on them.
Take a few precautions and you won't have to worry about thieves anywhere in Rome; leave valuables locked-up back at the hotel, only take enough cash for the day. Keep the cash and your cards in a money belt under your clothing, or in a secure pocket within a bag that you keep in front of you or over your shoulder - backpacks are a magnet to thieves and difficult to protect unless you have eyes in the back of your head. Men should keep wallets in a front trouser pocket, not a back one. If you feel strangers are too close to you (even in a crowd) do a quick check of your pockets and make it obvious you know about your security, if it is a pickpocket they'll move off to find a less aware target.... but don't be rude or aggressive, it might just be a stranger caught in a crowd with you.
Phil from the worldnomads.com safety hub over 7 years ago