The reason this book should continue to be taught, in my opinion, is that it is a very good book, first of all, and secondly it is part of the American literary tradition. No adventure story that I am aware of has had a similar life and impact as The Adventures of Huckleberry Finn has had. It is a pillar of the genre.
However, that does not mean that the book should be taught in 9th and 10th grades. I'd suggest that a certain degree of maturity is demanded of a reader if he/she is to understand the quality and subject matter appropriately.
The antiquated (and now offensive) racial discourse and racial characterizations do not disqualify the novel from maintaining a place in the cannon but should disqualify the novel from entering classrooms where students are not prepared to deal with the judgments and language of the book with a critical suspension of 21st century moral perspectives.
Mark Twain's The Adventures of Huckleberry Finn must remain part of the canon of American literature because Twain's wit and satire endures as part the American experience. After learning of his death, President William Howard Traft remarked,
Mark Twain gave pleasure--real intellectual enjoyment--to millions, and his works will continue to give such pleasure to millions yet to come....His humor was American, but he was nearly as much appreciated by Englishmen and people of other countries as by his own countrymen. He has made an enduring part of American literature.
There are so many contributions to Realistic American literature that Twain has made that teachers must not compromise by censuring his American classic. His use of dialect and regionalism, his portrayal of religious hypocrisy, social hypocrisy, the influences of technology, man's inhumanity to man--all these provide wonderful literary experiences as well as moral lessons. In The Adventures of Huckleberry Finn, for instance, it is Jim who is the most genuine, the kindest, often the wisest, and certainly the most human.
Too often political correctness is an insidious form of censureship. For example, President George Bush wanted Joseph Heller's great satire, Catch-22 removed from high school libraries because it satirizes government and especially military bureaucracy. After this book is censored, what is next? For, with censorship, there is no definitive line that can be drawn. Science-fiction writer Ray Bradbury remarked,
You don't have to burn books to destroy a culture; all you have to do is get people to not read them.
I assume that you are asking this because of issues with the use of the word "nigger" in the book. If so, I would argue that the use of the word should not prevent the book from being taught.
That word was widely used in the time in which this book was set and everyone knows it. It is not as if anyone is going to read the book and see that word for the first time.
It is also clear from the book that Twain is advocating a more equal relationship between whites and blacks. Given that much of the book is an argument for racial equality, why worry about the fact that it uses an offensive word (and the fact that the main black character speaks like an uneducated slave, which he was...)?