Mark Twain's The Adventures of Huckleberry Finn is regarded by many as the greatest literary achievement America has yet produced.
Featuring a child as the protagonist and narrator and using this child's voice - in the vernacular - is a first in American letters. The wit, irony, and adventure of the novel are additional literary elements that contribute to the classic status of this novel.
Though we may argue the question of whether or not this novel would become a classic if it were published today (most critics will agree that it would be a classic if published at any time), there is no arguing the question of this novel's significance and status in the American canon.
Novels like The Catcher in the Rye and To Kill a Mockingbird clearly draw from Twain's influence in works that feature a humorous but serious child narrator and protagonist. Also in these novels, we see an interest in tackling significant social issues of the day, an aspect of Twain's novel that is often commented upon.
A novel does not have to be flawless to be a classic. In a conversation like this one, this idea is sometimes important to consider. Books like 1984 and Moby Dick offer significant flaws in style and narrative decisions, yet remain very influential and culturally significant. These are classics with flaws. Their flaws, however, do not diminish their status as classics.
Huck Finn is considered an American Classic because it incorporates all of the aspects of American Culture into many "Adventures." From the dialogue of the unique characters in the book, to the interesting conflicts and puzzling questions posed in the book, everything about The Adventures of Huckleberry Finn relates to something in American Culture at that time, and in some cases even now! This is why it is a classic. For more specific examples from the book, message me.