American producers have bastardized many a delicious Italian cheese, producing bland and waxy knock-offs that no one with a palette would dare eat. Fortunately, Italy has some pretty strict cheese production and exportation requirements, so you can still find the real (and delicious originals). Beware of cheeses labeled Parmesan, instead pick those labeled Parmigiano-Reggiano (a name which is reserved by European law for cheeses produced in the regions of Reggio Emilia, Modena, Bologna, and Mantova). If you want something similar, but a little cheaper, go with Grana Padano or Piave.
My personal favorites from Italy are Pecorino Romano, Mozzarella di Bufala Campana and Ricotta Salata.
Pecorino Romano is another sharp cheese perfect for grating. It's made with sheep's milk (as is any cheese with the word Pecorino in the name) and a little smoother tasting than Parmigiano-Reggiano. I find it works nicely with a wider variety of sauces and pestos, and makes a positively decadent alfredo when tossed with pepper, butter, pasta and a small amount of cream.
Mozzarella di Bufala Campana is fresh mozzarella made from the milk of water buffalo rather than cattle. It has a tangy and rich flavor that's unlike any fresh mozzarella you've ever tasted.
Finally Ricotta Salata is standard Ricotta that has been salted and dried. The flavor is fresh and a bit salty. It's perfect for shaving on a salad or a lighter pasta dish.
