When I went to school, there were very few "must reads"; you weren't required to take English or American Lit; you could take other English classes which may require short reading but not novels. I think most American kids read Tom Sawyer and Huckleberry Finn (and even that may no longer be the case), but beyond that there's plenty of variety in what they read.
You will find a HUGE number of books in the lists below. Many are Greek and Latin classics which are rarely read today. The more modern fiction on those lists (The Prince, Moby Dick, etc.) are more commonly read.
http://en.wikipedia.org/wiki/Harvard_Classics
http://en.wikipedia.org/wiki/Great_Books
http://en.wikipedia.org/wiki/Great_B..._Western_World
http://en.wikipedia.org/wiki/Western_canon