The Library of Congress has its rather mundane list of 88 books that "shaped" America.
In most ways it is a list of "the usual suspects," from Washington Irving's "The Legend of Sleepy Hollow" to Harriet Beecher Stowe's "Uncle Tom's Cabin" to Mark Twain's "Huckleberry Finn" and Ernest Hemingway's "For Whom the Bell Tolls."
There is very little history, no science writing at all, only one piece of science fiction, and whole interesting segments of the American experience truncated without a consideration.
So here's my list of twenty-five necessary additions (OK it turned out to be 26--sue me):
Jonathan Edwards, Sinners in the Hands of an Angry God (1741). Stricly speaking, a sermon not a book. But absolutely critical to understanding American evangelical protestant religion.
Alexis de Tocqueville, Democracy in America (1835). Nothing in the rules for the list said the books had to be by American authors. De Tocqueville's insightful look at the American people from the outside is still arguably just as necessary as The Federalist Papers.
Charlotte Perkins Gilman, The Yellow Wallpaper (1892). This is actually only a 6,000 word short story, but the descent into madness has never been so adeptly caught in a piece of American fiction.
Frederick Jackson Turner, The Significance of the Frontier in American History (1893). Though he did not write a lot, the "Turner thesis" about the critical importance of the Westward movement to understanding America is still highly influential today.
Charles A. Beard, An Economic Interpretation of the Constitution (1913). Although now severely dated in terms of scholarship, this book revolutionized constitutional studies by attributing personal political and economic agendas to the hitherto pristine Framers.
Carl Sandburg's Lincoln (1928-1939). The epitome of the big literary biography from the 1920s and 1930s, Sandburg's work not only captured a genre and made history sing, but it also effectively created the image of Lincoln as we know him (or at least think we do) today.
Ring Lardner, Round Up (1929). One of the best and least heralded American short story writers of his own or any later time.
Jon Dos Passos, USA Trilogy (1930-1936). Experimental fiction adroitly retelling the American story (if you liked this, try John Brunner's magisterial sci-fi novel that uses the same narrative tactics, Stand on Zanzibar).
Carter G. Woodson, The Mis-education of the Negro (1933). Still highly relevant today, and far better written than anything by WEB Dubois.
Sinclair Lewis, It Can't Happen Here (1935). Not necessarily his most well-known novel, but seminal in terms of the creation of an entire dark genre.
A. B. Guthrie, The Big Sky (1947). Although I am also partial to Louis L'Amour, Zane Grey, and even Terry Johnston, nobody has ever captured the Mountain Men better than Guthrie does in this novel (and you should also read The Way West.)
Robert Ruark, The Old Man and the Boy (1957). THE classic of growing up in rural America.
Paul Horgan, A Distant Trumpet (1960). If you have seen the old John Ford westerns ("She Wore a Yellow Ribbon," "Fort Apache," etc.) then you must also read this book.
Tom Wolfe, The Electric Kool-aid Acid Test (1968). Wolfe never wrote anything any better than this (including The Right Stuff), which is a damn shame since this experimental work chronicling the misadventures of Ken Kesey's "Merry Pranksters" happened at the beginning of his career.
T. R. Fehrenbach, Lone Star: A History of Texas and the Texans (1968). Almost a primer in how to write history (I had a hard time choosing this over his amazing book on the Korean War entitled That Kind of War, which equally deserves your attention).
Eldridge Cleaver, Soul on Ice (1968). If you want to understand Black Power and black anguish, go here.
Kurt Vonnegut, Slaughterhouse Five (1969). An awful lot of Vonnegut is crap, but this novel is far more deserving of being placed on a list of influential books that happened to be science fiction than either Bradbury's Fahrenheit 451 or Heinlein's Stranger in a Strange Land.
Philip K. Dick, Ubik (1969) An incredible classic work of Sci Fi by one of America's best and most tortured novelists. Compared to Dick (The Man in the High Castle, Do Androids Dream of Electric Sheep, Martian Timeslip, and many more), Hemingway was a well adjusted optimist.
Harlan Ellison, The Glass Teat (1970). If I wanted to include Harlan Ellison as Sci Fi writer I'd have to choose something like "A Boy and his Dog" or the anthology Alone Against Tomorrow. But Ellision is also one of America's priemere essayists, and so I go with this collection about modern television.
Ron Glasser, 365 Days (1971). Simply the best, most human book ever likely to be written about the Vietnam War. Do NOT read the last chapter if you are even slightly depressed or don't have the time to think about the consequences.
Carl Berntsein and Bob Woodward, All the President's Men (1974). This is the book by the guys who brought down Nixon.
Lawrence Goodwyn, The Populist Moment (1978). This is Goodwyn's shortened, popular version of his Democratic Promise that is still the definitive history of the Populists. Great writing, and Eric Foner really wishes he could be Goodwyn when he grows up.
Joel Rosenman, John Roberts, and Robert Pilpel, Young Men with Unlimited Capital, The Story of Woodstock (1979). Not just the story of Woodstock, but the story told by the guys who thought it up and brought it off (sort of).
William Cronon, Changes in the Land, Indians, Colonists, and the Ecology of New England (1983). This book singlehandedly created mainstream ecological history, at least as applied to American history.
Martin Duberman, Stonewall (1993). The definitive history of the Stonewall Rebellion that created the modern gay rights movement.
Rebecca Skloot, The Immortal Life of Henrietta Lachs (2010). Quite simply the most amazing book on science, and capitalism, and race in America, and human suffering, and unbelievable science you may ever read. No wonder it stayed on the NYT bestseller list for two years.