In France, every interaction starts with a "bonjour" (or, if it's past about 5 PM, a "bon soir"). It doesn't matter how small the interaction is: buying a baguette from the boulangerie or asking for directions, you start every conversation with a hello. To not say hello is very rude; I suspect that, when people talk about how rude the French are, it's partly because they don't know this basic facet of the culture.
In Italy, you don't necessarily say "buongiorno" when you greet someone. In fact, on the phone, you don't start with "hello" at all, but "pronto" - essentially, "I am ready, speak to me." But if what I have seen in the past few weeks is typical, you always say goodbye. When you leave a restaurant or shop, you are sure to hear "arrivederci." And, just for good measure, you'll probably also hear "grazie," "buona giornata" or "buona serata" (have a good day/evening), and "ciao." You may hear each of these goodbyes from every person you pass as you leave.