I've seen this in Paris, France, Barcelona, Florence... any popular tourist destination will have petty thieves.
These scams vary, and you should read about them before you go, to be aware of them. Some of the ones I've seen:
People in period costumes (mostly Roman centurions) will accuse you of taking photos with them and demand an exorbitant amount of money for the pictures.
People will try to slip an object or a flower into your hands and then demand money. You might have to say " no " very aggressively.
Someone will approach you with a map and ask for directions (their accomplice is behind you while you're distracted, he steals from you).
Someone will place paintings on the ground near monuments like cathedrals, and when you inevitably step on one (because you're looking at the Duomo, not the ground) they'll demand an absurd amount of money for the painting you just stepped on.
Basically, you just have to understand that if you're a tourist in a city, nobody will have a good reason to talk to you. Nobody needs directions from you, nobody needs your signature on a petition; someone trying to stop and talk to you in a major tourist destination is probably up to a scam.
If you find yourself in a situation where someone is demanding money from you (maybe you stepped on a painting or removed that ill-advised painting with the Centurion), simply say:
"Okay, let's find a police officer and I'll pay you in front of the officer ." This usually makes them back down quickly.
Perhaps you have to be aggressive to prevent people from touching you or putting anything on you.
And also, be careful with your belongings. Don't leave your phone on the ground next to you while you're having a picnic by the Seine. It's all about not being an easy target – that's enough to deter people.
That being said, don't let the fear of being robbed stop you from traveling ! Rick Steves has a story about a family who had their passports and thousands of dollars stolen immediately upon arrival in Amsterdam , and they still had an amazing trip .
Simply be aware and have a plan in case the worst happens.