Gentlemans Agreement by Laura Z. Hobson
Something by Zane Gray
Something by Howard Zinn (A People’s History of the United States, maybe)
For a more pastural setting and a slice of Americana:
Lemon Jelly Cake Madeline Babcock Smith
Never miss a sunset Jeanette Gilge ( for ages 10 and up.) (It is one of a series.I haven’t read the rest, but I adored this book as a kid.)
Little House On the Praire Series Laura Ingalls Wilder. (ages 9 and up)
Anything by Dave Barry for some funny, lighter side reading.
And we would be remiss to exclude the Master: Cecil Adams The Straight Dope, The Return of the Straight Dope and The Straight Dope Tells All. A must for all discriminating libraries.
I never realized until this thread and checked my personal stash of books that most of my fiction and non-fiction books are set in the UK. Interesting.
If this has been mentioned, forgive me.
Catch 22
Sunshine Soldiers by Peter Tauber. recently back in print. I remember it as hysterically funny when I read this story about a reservists account of boot camp during the Vietnam war. I was 14 and a girl (still am), but it was a scream to me then and I lost my copy that I (cough)stole (cough) from my school’s library. Karmic payback, to be sure.
What about spy, mystery or war novels? It certainly is not my genre, but I am sure other dopers can recommend a few good page turners.
For a much lighter side of mystery:Janet Evanovich’s Stephanie Plum Novels are a stitch. they are also like crack on a pringle. Can’t have just one.
If you need recommendations for cheesy romance stories, or even better than average romances, I’m your gal. 
Random recommendations that haven’t been mentioned AFAIK:
**Sophie’s Choice ** - William Styron
Long Day’s Journey into Night - Eugene O’Neill
Cat on a Hot Tin Roof - Tennessee Williams (I’m assuming plays are o.k.)
Bastard Out of Carolina - Dorothy Allison then,
Me Talk Pretty One Day - David Sedaris, to lighten things up
Come To Me - Amy Bloom (very beautiful short stories)
Look Homeward Angel - Thomas Wolfe
Tender is the Night - Fitzgerald
A Prayer for Owen Meany - John Irving
for kiddies: Where the Wild Things Are - Maurice Sendak
Yes, all the Straight Dope books need to be included.
I’d suggest Thomas Paine’s Common Sense and The Rights of Man. The former is more focused on the gripes of the colonies, but the latter is broader and had a great deal of influence on world events.
One Flew over the Cuckoo’s Nest - Ken Kesey
Guns, Germs and Steel - Jared Diamond
Deliverance - James Dickey
Last Picture Show - Larry McMurtry
Breakfast of Champions - Kurt Vonnegut
(I would include a number of books by Vonnegut, but at least this one and Slaughterhouse 5, already mentioned)
The Maltese Falcon - Dashiell Hammett
The Caine Mutiny - Herman Wouk
The Demon-Haunted World - Carl Sagan
Call of the Wild -Jack London
Ballad of the Bones - Byron Herbert Reece
The Season of the Flesh - " "
Bow Down in Jericho - " "
The Complete Short Stories of Ernest Hemingway
D-Day - Stephen Ambrose
Any good collection of the stories of H.P. Lovecraft
You probably need several good comprehensive collections of science fiction short stories.
Also, given the purpose of the collection (to familiarize Sri Lankans with American culture), I would suggest that you need not just the high-brow, capital L “Literature,” but also some best-sellers from the past few decades. Just a thought.
Also, given that purpose, maybe some photography collections, and some histories of popular music, art and cinema in the US. Maybe a history of the automotive industry.
Early settlement/colonial stuff:
The History of Plymouth Plantation, William Bradford
The Tenth Muse Lately Sprung Up in America, poetry by Anne Bradstreet
Governor John Winthrop’s Journal
Letters from an American Farmer, Hector St. John de Crèvecoeur
Sketch Book, Washington Irving
Poetry of Phillis Wheatley
The letters of Abigail Adams to her husband
Most of these can be found in anthologies of early American writers, like:
Early American Writing, Giles Gunn - Editor
672 pages | ISBN 0140390871 | Feb 1994 | Penguin Classic
Later stuff:
Narrative Of The Life Of An American Slave, Frederick Douglass
The Narrative of Sojourner Truth: A Northern Slave
Declaration of Sentiments from the Seneca Falls Conference, Elizabeth Cady Stanton
Diaries of Mary Chesnut
Poetry of Langston Hughes
To follow up on spoke-'s suggestion about photography, how about books with the photographs of Ansel Adams, or the WPA photographers like Dorothea Lange.
Books on art from the Ashcan or Hudson River School artists.
I second A People’s History of the United States
Perhaps the best single book to balance Hollywood’s picture of the U.S. that people there are certainly getting.
also
The Autobiography of Malcom X
important historically, and as a rounded view of the U.S.
Little Big Man and Catch 22 also come to mind, but neither are as important.
Not everyone will agree with these i’m sure (trying not to repeat what others have offered already):
Atlas Shrugged and The Fountainhead by Ayn Rand
The Shining - Stephen King
The World According to Garp - John Irving
A Fool’s Progress - Edward Abbey
For Whom the Bell Tolls - Hemmingway
Watch For Me On The Mountain - I forget the author, but this is the story of Geronimo
Bury My Heart at Wounded Knee - Again I forget the author
More kiddie lit:
Charlotte’s Web - E.B. White
Where the Red Fern Grows - Wilson Rawls
Old Yeller - Fred Gipson (as long as we’re killing off family pets)
Island of the Blue Dolphins - Scott O’Dell
The Phantom Tollbooth -Norton Juster
You know, the more I think about it, the more I think kiddie literature expresses what is best in Americans, that to which we aspire. (I suppose that is because many of these books are designed to teach ethical lessons.)
If you look over the more adult-oriented literature in this thread, a lot of it has themes of disillusionment at our failure to live up to those aspirations.
With that in mind, one more classic piece of kiddie lit:
My friend Flicka - Mary O’Hara
Hmm, I’m suprised that no-one has recommended any books regarding sports. Two that come to mind are:
The Boys of Summer by Roger Kahn and The Historical Abstract by Bill James.
A few more that should get a sense of “Americana” or of an American worldview:
A Bright, Shining Lie by Neil Sheehan - perspective on the Vietnam War
Devil’s Dictionary by Ambrose Bierce
Any of the writings of H. L. Mencken
Select writings from pragmatists (US’s contributions to philosophy) such as James, Peirce, Dewey.
The next two many would not consider good works (in a literary sense), but nevertheless were hughly successful and may prove useful in getting some insight into the American psyche:
How to Win Friends and Influence People by Dale Carnegie
The Power of Postive Thinking by Norman Vincent Peale
The Ugly American by William Lerderer, et al. - dated, but I think extremely relavent given current events.
Black Like Me by John Howard Griffin - again dated, but does illustrate how much race/racism is a part of American history.
Silent Spring by Rachel Carson - also dated, but helped propel the environmenal movement in the US.
By John Steinbeck: “The Grapes of Wrath” “In Dubious Battle” “Of Mice and Men” “The Long Valley” and his other short story collection, which I can’t think of at the moment, “The Moon is Down” “East of Eden”
TC Boyle’s “Stories” is highly recommended.
Everything else has been said already that I can think of.
The Yearling by Marjorie Kinnan Rawlings
I didn’t see these mentioned–they may have been I speed-read the list.
Let Us Now Praise Famous Men James Agee & Walker Evans
The Kandy-Kolored Tangerine Flake Streamlined Baby Tom WolfeThe Redneck Manifesto Jim Goad
(and since I always want to write his name as Joad that reminds me, Grapes of Wrath has to be on here, right?