Now that Fried Dough Ho mentions Laura Ingalls Wilder, it occurs to me that Little House on the Prairie is an excellent suggestion, also.
And personally, I’m not really thinking in terms of what books are best, per se, but which books provide the best cross-section of Americana. I’m as big an Asimov as anyone, but Foundation, say, isn’t really about America in any sense except possibly a weak allegory.
A Fable just felt the most approachable to me of the Faulkner I’ve read. I think for one, while the details might be challenging to follow, the basic plots (war is hellish, a Jesus allegory) were more familiar to me than in some of his other works; and two (trying to figure out how to explain it clearly): I’ve found thus far that, to me, almost all his work feels vaguely surreal (e.g., I’ve never spent any time in the old deep south hunting bear or dealing with racial issues, so Go Down, Moses feels somewhat other-worldly to me), but A Fable is fairly up-front about that - it’s the point, I think? As I said, I’ve struggled a lot with him, so it could just be me, but I guess it feels more accessible than some of his other novels.
(But I also don’t know that I believe Faulkner himself when he says that Go Down Moses is one novel and not a collection of stories, so I might just be missing his point entirely.)
Tom Sawyer/ Huckleberry Finn - Twain- should be read one after the other, both great
For Whom the Bell Tolls - Hemingway - my all-time favourite book
Gravity’s Rainbow- Pynchon - mental and dense - worth many rereads
To Kill a Mockingbird - This is a given, an astonishing work
The fifth is a bit of a tie:
Underworld - Don DeLillo - The opening sequence at the baseball game is the most cinematic and evocative thing I’ve ever read. It is fantastic, his prose works like one of those cameras that swoop up and down the field and around the stands. The trouble is the rest of the massive tome is pish in comparison. Still, what a writer,in parts.
Bonfire of the Vanities - Wolfe - He’s only written two good books (The Right Stuff is the other obv.) but this one has such electric dialogue.It charges on, relentless.
Old Man and the Sea (or other by Hemingway)
Call of the Wild (or other by London)
Bonfire of the Vanities (or other by Wolfe *)
Huck Finn (or Sawyer)
something by Steinbeck
I preferred Norris’ Octopus to Sinclair’s Jungle. Many of those mentioned in the thread are on Wikipedia’s list. I’ve read about one-third of that list, didn’t like Great Gatsby, and hated the one of Passos’ USA Trilogy I read.
The Last Picture Show - Larry McMurtry
Cold Mountain - Charles Frazier
Winesburg, Ohio - Sherwood Anderson
Of Mice and Men - Steinbeck
Huckleberry Finn - Mark Twain
My focus, in making a list like this, tends to be more historical than literary. It’s also one of those things, like “5 favorite movies,” where my list would probably change every time you asked me.
Still, here one possible list:
Melville - Moby Dick
Twain - Tom Sawyer
Sinclair - The Jungle
Steinbeck - Grapes of Wrath
Wright - Native Son
Of course, the fact that i have no post-WWII novels on my list makes the whole exercise a bit silly. The fact is that reducing a list like this to 5 is basically impossible.
There’s a non-fiction book that i think could also easily go on the list: The Education of Henry Adams, by Henry Adams.
Are we counting Lolita as an “American” novel? I would, and if so, that’s top of the list for me. Follow that with Huck Finn, Catch 22, Great Gatsby, and Sound and the Fury.
Reviewing my own list (and my syllabus… back to school tomorrow!), if I could suggest plays instead of novels I’d definitely remove Catcher in the Rye and replace it with Death of a Salesman instead.
Although To Kill a Mockingbird is one of my all-time faves, it is taught at the 8th grade level in my district, so I don’t get to teach it to my juniors.
Cool, thanks for the explanation. I often find Faulkner frustratingly opaque (which is my problem, not his) and that book has been especially difficult for me to tackle, so it’s nice to know that someone other than the Pulitzer committee of 1955 has found it worth reading. 
Moby-Dick
Emerson’s essays
D.H. Lawrence’s Studies in Classic American Literature
Bellow, Adventures of Augie March
Ralph Ellison, Invisible Man
There are some good suggestions in this thread. But Fitzgerald’s milquetoast prose feels like only one step beyond Anglophilia, and Faulkner’s vision of America lives in a few Southern counties and nowhere else. If you want some really muscular American prose, try:
Norman Mailer, The Naked and the Dead
Jim Thompson, The Killer Inside Me
Ha! One of those Brits who can’t even pronounce their names like they’re spelled.
In semi-seriousness…
“At the Mountains of Madness” by H. P. Lovecraft.
Sure, it’s pulp fiction, but it’s pulp fiction that’s stood the test of time. While the majority of Lovecraft’s pulp contemporaries have disappeared from the public consciousness, he retains a large influence on modern pop-culture.
And his writing is very, very “Yankee”.
i will agree that DoaS is a powerful and depressing play but i remember as an 11th grader that “raisin in the sun” moved me deeper than “death of a salesmen.” so did “the glass menagerie.” maybe it’s because i was personally more disposed to connect with racism and ostracism than unfulfilled dreams. i’d like to think it’s because of my age rather than my own personal insecurities.
We have to, don’t we? Otherwise the Ayn Rand suggestions above would have been laughed out of court.
As someone whose fiction reading primarily constists of mysteries and science fiction, here’s a list:
To Kill a Mockingbird
Huckleberry Finn
An American Tragedy
Cannery Row
and - any random Hemingway in order to realize just how excruciatingly uninteresting his writing really is.
A novel written by a Russian, first published in France, written in English? Why not? 
Huh. I’m about 150 pages into Moby Dick (and have been for about three weeks), and his sense of humor seems quintessentially American to me, as does his almost self-satisfied acceptance of people from different social classes–even savages–as his equals.
I was thinking about the challenge from a different perspective: are there genres that America dominates, and if so, what would be some good and representative examples from the genres?
The ones I could think of, with suggestions:
-Westerns: nobody does these like we do. Lonesome Dove, maybe (which I haven’t read), or get some current flavor plus some fantastic literature in with some Cormac McCarthy, maybe even Blood Meridian.
-Horror: others do it, but between Poe and Lovecraft, we can make something of a claim for turning it into a genre. Maybe At the Mountains of Madness.
-Hard-boiled detectives: Brits have the brain-teaser-mystery category sewn up, between Doyle and Christie, but I think America has a lock on hard-boiled detective stories. The Big Sleep is my favorite by my favorite author in this genre, Raymond Chandler.
-Science Fiction: We didn’t invent it, but we damn sure popularized it, and it’s a major, major influence on global culture by now. I’m thinking Left Hand of Darkness for some reason.
-Road Trips: Obviously other folks have done them (Canterbury something or other, I seem to recall…), but they’re a staple of American fiction. Be a purist and go with Dharma Bums, or stretch the genre a little to allow one of the classics: Huckleberry Finn.
Obviously this isn’t a list of the Five Greatest American Novels, but I think it’d provide an interesting overview to some of the more influential strains within American literature.
I teach Raisin in the Sun as well. I taught The Glass Menagerie in my Theatre Arts elective. I had several students choose to write their final papers comparing and contrasting Willie Loman and Walter Younger and their interpretation/struggle for the American Dream.
Whew, Larry McMurtry mentioned twice on this list so I’ll pipe up :).
Lonesome Dove is a must-read, even if it’s not included as part of a “top five American novels”, it’s compelling and ten years after my initial read, I still think about the characters often.
I do think The Scarlet Letter and Huckleberry Finn belongs on the list, and I would include Of Mice and Men as well, although maybe Grapes of Wrath is a better choice, I prefer OMAM.
If you want the Official, Dead-white-male style canon of the five Greatest American Books, my impression is that they’d be (in chronological order)
(Note that Walden is non-fiction. It’s a “great book” but not a novel.)
These are not necessarily the most popular or widely-read. For example, The Adventures of Tom Sawyer may well be more popular and more entertaining than Huckleberry Finn, but it isn’t as deep or as Great as a Work of Literature. But at any rate, you must read something by Twain: if there is such as thing as the Great American Author, he is it.
The list above leans toward the 19th century, maybe because those older books have had more time to establish themselves as part of the canon. A more-recent-leaning list might well include Hemingway (who some say was at his best in his short stories), Steinbeck, and Faulkner (who can be fairly difficult), or maybe at least something by an African-American author (like Ralph Ellison’s Invisible Man).
But really, you should read To Kill a Mockingbird. Most people who read it like it; it’s some people’s favorite book; and it’s very American.
Wow, I’m shocked at a couple of trends:
This begs the question: is academia advanced enough to accept sci-fi/horror as “literature?”