Lots of good answers here -- I'd throw in anything chosen by some teacher or school system because of the gender, race, sexual preference or politics of the writer (anything by Toni Morrison, for example, who is probably the most overpraised and over-awarded American writer in history.)
But, The Great Gatsby? I could read certain passages from that once a month the rest of my life and never tire of it. As Ernest Hemingway said of F. Scott Fitzgerald, "His talent was as natural as the pattern that was made by the dust on a butterfly’s wings."
Take this one line near the end, when a character muses on what it must have been like to see the American East Coast from an early exploring ship:
"And as the moon rose higher the inessential houses began to melt away until gradually I became aware of the old island here that flowered once for Dutch sailors’ eyes—a fresh, green breast of the new world. Its vanished trees, the trees that had made way for Gatsby’s house, had once pandered in whispers to the last and greatest of all human dreams; for a transitory enchanted moment man must have held his breath in the presence of this continent, compelled into an æsthetic contemplation he neither understood nor desired, face to face for the last time in history with something commensurate to his capacity for wonder."
What words ever better summed up what America has meant, as an idealized vision, to generations here and around the world?
It may be because I live within a few miles of where Fitzgerald is buried in a small Catholic church yard, now hemmed in by a bustling, noisy highway lined with strip malls and fast food joints. I find myself pulling off the road and into the church yard on a whim several times a year, just to spend a couple minutes there. On his tombstone is the famous last line of Gatsby: "So we beat on, boats against the current, borne back ceaselessly into the past."