Take, for example, Harper Lee's 1960 masterpiece To Kill a Mockingbird. Although the story's setting is a few states and about a century off, the novel can be seen as a 1960's retelling of Twain's classic. Let's compare.
Starting with the obvious stuff, Huckleberry Finn is narrated retrospectively by its young central character, Huck, who furiously resists becoming "civilised." Likewise, To Kill a Mockingbird is narrated by its young central character, Scout, who's up in arms against having to become "ladylike." Both Huck and Scout have that wisdom-of-the-innocent thing going, making them great candidates for a time-traveling spinoff of Kids Say the Darnedest Things.
Huck spends the beginning of the tale evading his father, an abusive alcoholic who serves as the novel's moral red light before winding up shot in the back. Although Scout's own father falls at the opposite end of the moral spectrum, the analogous character is Mayella Ewell's father, an abusive alcoholic who winds up stabbed through the ribs. Neither death is particularly heart-wrenching.
After running away from his father, Huck befriends Jim, an escaped slave on the social fringe. As their relationship progresses, Huck learns to outgrow his social conditioning and see Jim as an equal. Scout's experience is slightly more complicated. Although a wrongfully confined black man features heavily in Scout's moral development, the relationship that more directly parallels Jim and Huck's is with Boo Radley, the local shut-in. Like Jim, Boo is a social outsider who has gone into hiding. By befriending Boo, Scout learns to make her own decisions about people rather than accept reputation at face value.
One of the most morally-loaded moments Huck witnesses as he travels down the Mississippi is the attempted lynching of a local sheriff. Unimpressed, the sheriff shames the angry mob out of attacking him by pointing out that no one has the guts to confront him as individuals. After he insists that "a MAN'S safe in the hands of ten thousand of your kind-as long as it's daytime and you're not behind him," the crowd scatters. Similarly, Scout witnesses an angry mob attempt to bully her father in the middle of the night. In response to their threats, an unafraid Atticus responds, "Do you really think so?" All it takes to get the men to leave is the intervention of Scout and her twelve-year-old brother.
Both novels end on the same crucial note. When Huck's personal hero, Tom Sawyer, is shot in the leg, Jim steps forward to save him, thereby forfeiting both his anonymity and his freedom. Likewise, when Jem, Scout's older brother and idol, has his arm broken by Bob Ewell, Boo comes out of hiding to protect him and risks going to jail for murder.
Both Twain and Lee use the naivetÃ© of children to make huge moral arguments about racism, social conditioning, American history, and the essential goodness of man. As for the claim that there's been no good literature since Huck Finn, we think Ernest Hemingway has some homework to do.