In the realm of classic literature, there are a few American names that spring to mind. Let us proceed chronologically.
19th Century: Poe, Twain or Melville are the only ones who stand a chance of being called the greatest American writer. Huck Finn is one of the most influential books in our history. Moby Dick alone means the latter has a pretty good shot.
20th Century: Modernists: Hemingway, Fitzgerald, Faulkner. I am partial to Hemingway. And although Fitzgerald wrote the best American novel of the 20th century (The Great Gatsby), Tender is the Night is his only other work that can be called truly excellent. Both Faulkner and Hemingway won the Nobel Prize in Literature, but I would argue that Hemingway did more to change the face of the American novel. His lapidary style in The Old Man and the Sea is Biblical. We could also mention Salinger and Bellow in this discussion.
Postmodernists: I have ranked the following authors in tiers since not enough time has passed to truly measure their greatness:
In the top tier: Pynchon, Updike, Roth. Gravity’s Rainbow is arguably as devastating to fiction as was Moby Dick. Updike wrote a lot, but he will always be remembered for the wonderful Rabbit Tetralogy. And Roth is similarly masterful, and has a number of novels that could be called masterpieces. Toni Morrison is also a contender, she won the Nobel Prize in 1993.
Second Tier: McCarthy, DeLillo, Mailer. These guys have all written great novels, but The Naked and the Dead is a war novel and too limited in scope. White Noise is a contender. And I’m reading Blood Meridian right now. It’s hard to assess authors who are still producing, but if I missed anyone, let me know. And feel free to make your case for your favorite.