Mind you, our trip was all cities—Rome, Florence, Venice, and a day trip to the Amalfi Coast and Pompei. We were very glad NOT to have had a car. Walking was easily the best way to get around the cities with the occasional Uber. On advice from Cougarboard, we forewent a rental car for the Positano trip and were glad we did.
Between traffic congestion, parking, convenience and some insanely aggressive driving (one cab driver got in an accident with us in his car, and he wasn’t the worst one), we were very glad to have skipped the rental car. But we weren’t out seeing the countryside either. A train seems sufficient for this as well, but I could see why people would want the freedom of a car if you’re going to be exploring the countryside.