Much of the most important American fiction fits more comfortably into the the category of "romance" than realism. (The term goes back to the medieval narrative form, and doesn't have any connection to the modern "romance novel.") Hawthorne famously set out the terms in which the romance is to be understood in his preface to The House of the Seven Gables: "When a writer calls his work a Romance. . .he wishes to claim a certain latitude, both as to its fashion and material"; this "latitude" allows him to present the "truth" of human experience "under circumstances, to a great extent, of the writer's own choosing or creation" and to "manage his atmospherical medulm as to bring out or mellow the lights and deepen and enrich the shadows of the picture."(The rest of the post is very much worth reading, too. I highly suggest you abandon me and head over there. Daniel Green has written some excellent non-blog articles, as well, including the fascinating "Empty Rhetoric: Innovative Fiction and the American Literary Magazine".)
Going back to the beginnings of American fiction, "romance" would thus encompass the work of Charles Brockden Brown (often identified as the first important American novelist), Washington Irving, James Fenimore Cooper, Hawthorne, Melville, much of Twain, the later Henry James, Faulkner, Ellison, Flannery O'Connor, Malamud, much of the later Roth, and, in my opinion, almost all of the writers called "postmodern." Of the "great" American writers, only Crane, the earlier James, Edith Wharton, Dreiser, Steinbeck and Hemingway could plausibly be called "realists." (And there are those who think the latter would more aptly be called a "symbolist" rather than a realist.) Currently the followers of Raymond Carver or Richard Yates might fit the description.
I tend to cringe whenever I hear the word "realism" applied to art of any sort, not because it's necessarily an inaccurate label, but because of the assumptions which so often fuel its use. There is a sense that realism is not a style, but rather a default setting for "good" fiction, but, as Green shows, this assumption is not based on a very thoughtful reading of literary history. Lacking anything better to say, the commissars of taste trot out the grand virtues of whatever they consider "realistic" and then use these delusional criteria to marginalize anything which doesn't suit them at the moment. (Scott Edelman recently looked at how such criteria have affected the critical reception of Jonathan Lethem's The Fortress of Solitude.)
In truth, realism is a style, most elements of which gained prominence in the 19th century, and which has never been the primary force for fiction. That so many people cling to the myth of "realistic" fiction's historical dominance is bewildering, because there are far more paths to understanding reality than that of the dim, dull, dreary byway of circumscribed imagination.