Registration makes it easy to contact you in an emergency or if somebody back home is desperately in search of you. Registering allows people to find you in case of emergency. It also gives you updated information on travel and security throughout Italy. You've heard the rumors and chuckled at the clever street urchins in Italian films, but you've assumed it was all exaggeration. Well, actually, no, it isn't.
Petty thievery is rampant, especially in urban centers and tourist meccas.
And don't struggle with a thief - he usually wins. There is some good news. The incidence of violent crime is quite low in Italy, lower still against tourists. Basically, you'll leave with your life but not necessarily with all your stuff. Tell them you want to report a furto.