I didn't try it. According to the rules, to use wi-fi in a bar you need to show ID and be registered, and they give you a login. Although I didn't try it, there's wi-fi in parks in Rome, where as I understand you give an Italian cell phone number, and they send something to the phone to confirm the login, and that links you to the ID you gave when you got the SIM card.
We used the Rome airport wifi in the Business Lounge. I think it is available in the whole airport though. I had to enter an Italian cell phone number and then they sent a message with a login name and password to the phone. There was another option to pay 0.50 eurocents if you didn't have a phone but I didn't do that so I don't know how that works. Maybe enter a credit card number?