Some front desk employees will just take your passport and write down your name and number on a separate piece of paper and give it back to you immediately. Sometimes, if they are busy and espcially if there is a line checking in or out, they will ask to keep it so they can collect the information later. I have never heard of anyone losing a passport by leaving it with the hotel. They usually will ask you to pick it up after you've unpacked and settled in your room.
The hotel is required to report the identity of anyone staying in their establishment to the local police. In fact, the law states that if you're not staying in a hotel or other commercial establishment where they report your whereabouts to the police, you're supposed to do it yourself at the local questura within eight days of your arrival in Italy.
It's actually illegal for anyone to be in a hotel room who isn't registered in it.....not that this rule hasn't been broken! ;-) An Italian friend told me the regulation is related to anti-terrorist legislation passed during the 1970s.

