Like any city in the whole world, crime is a problem....I have had a problem in Amsterdam, and someone else could have had a problem in say Rome...
Out and out robbery is something you should not put at the top of your list for worring about, watch out for pick pockets and bag stealers..these people are crafty, sneaky and you will not even see it coming...and they are in EVERY city...Always know where you wallet is, try to keep it under your cloths, and do not expose its location in front of others cause you never know who is watching. Here are a couple links from a prior discussion on other scams against tourists...
Don't Try This
Bad to Worse