I can think of a few
Although, I'm not sure if this is accurate information, because maybe some of the Italian foods are cooked, say.. in New York, some in London, some in Germany... Many Italians have chosen to emigrate, plus the kitchen influences are starting to spread a lot lately
But, here's what I have personally been missing out, before I came to Italy:
Torta Fritta - such a simple food, flour, water (or milk), salt fried in grease. Served with a bunch of salami and a glass of wine, makes the perfect snack!
Pesto - this is one of those foods that are already famous worldwide, but I have tasted in Italy for the first time. Not knowing what the heck it was, I used it on sandwiches
(like, instead of butter). Then found out it's great for pasta dishes!
Cotechino with lentils - it's some kind of boiled salami, served with a side of lentils. It's an Italian traditional food served at New Year's.
Mozzarella - sounds weird... but Italian mozzarella is to die for! I've bought it at home, when I went to visit, my sister has bought it as well but after tasting the one made in Italy, the other ones are plain awful..
Piadina - it's sort of a flatbread, cooked on a terracotta, folded in 2, containing vegetables, salami, cheese, sauce, whatever you like. I've tried eating it outside of Italy... it was awful!