The Divine Comedy by Dante Alighieri and The Bethroted by Alessandro Manzoni are a must in pretty much all schools here, and teachers will usually make you read them in full. As for everyone else, we usually read bits and pieces from different authors, including but not limited to: Francesco Petrarca, Giovanni Boccaccio, Ludovico Ariosto, Carlo Goldoni, Ugo Foscolo, Giacomo Leopardi, Gabriele D'Annunzio, Giovanni Verga, Giovanni Pascoli, Italo Svevo and Luigi Pirandello. Oh, and there's also Homer and Virgil, of course
Some teachers will also give you books to read, though that really depends on teachers themselves. For example, during my first two years in high school our teacher gave us to read The Late Mattia Pascal by Luigi Pirandello, To each his own by Leonardo Sciascia, The path to the nest of spiders by Italo Calvino and Murder on the Orient Express by Agatha Christie... then, at the beginning of the third year, we got a new teacher who wouldn't even bother with the mandatory Divine Comedy, let alone giving us books to read -____-
From what I could see, things are still pretty random nowadays too: I've seen my students bringing to school pretty much anything from Fight Club by Chuck Palahniuk to the whole friggin' Decameron by Giovanni Boccaccio (1000+ pages) ò___ò