Almost every town in Italy has some sort of Christmas cake, cookie, or pie. Here's a quick rundown of some of the best known, in order (roughly) of popularity. In case you were wondering, my personal favorites are Panforte and Pandoro.
Panettone is the traditional Christmas Cake of the Milanesi, and has become the most common Christmas cake in Italy thanks to its keeping qualities -- Industry can churn them out and they stay fresh. So industry does, and pastry shops everywhere also make them. It's a deserved popularity, because it is good, and if you make it yourself you can include exactly what you want -- raisins, candied fruit, and so on. Panettone is also easy to rework.
Pandoro is Verona's answer to Panettone, a rich, buttery cake that's generally sprinkled with an abundance of powdered sugar. Unlike panettone, it never contains candied fruit, and for some this is a plus. It is remarkably good in any case.
Struffoli (they're always plural) are fried dough balls dipped in a honey syrup, shaped into a wreath, and sprinkled with diavolilli, a type of candy. Sounds (and is) quite rich, and is also probably extremely old -- this sort of use of honey as a sweetener dates back to the Romans.
Some say Panforte is so good it allowed a Novitiate nun to drive the Devil from her convent, while others say it's older still, the centerpiece of the feast the Baby Jesus prepared for a street urchin who gave him his last crust of bread. Could be either, but it's good regardless.
Some associate caggionetti with Naples, but these fried cookies are made in other parts of the South as well.
These traditional Neapolitan Christmas cookies are S-shaped. For two possible reasons: First, in the past they were called sesamielli, and covered with sesame seeds. Second, they were (and are) also called Sapienze, because they were made by nuns of the Monastero della Sapienza.
Mention amaretti, and many think of the little, crisp, tinned almond macaroons one finds for sale in supermarkets. However, there are many variations; in particular, in many areas the freshly made amaretti sold in pastry shops are soft and chewy (the only requirement for amaretti is some bitterness, generally from almonds or peach pits, to offset their sweetness). Senesi add some orange when they make ricciarelli, and the results are extraordinary.
Dough, fried quickly and dipped in honey. Sounds simple, but they're very good.
Buzzolai are ring-shaped cookies, and were an essential part of every festivity in Dalmatia, in part because their round shape brings coins to mind, and in part because they're quite tasty. Every family had a recipe for them, and they vary greatly. Here are a couple, one simple, for Christmas Eve, and one much more complex, for Christmas Day.
Rich, tasty Calabrian cookies.