Here, we'll highlight just a few.
The Great Gatsby, by F. Scott Fitzgerald was challenged at the Baptist College in Charleston, South Carolina (1987). This book was challenged because of language and sexual references in the book. Maybe your book club would enjoy discussing this element of the book's past. Or check out a movie adaptation of this American classic.
The coming of age tale, The Catcher in the Rye has been challenged numerous times. Salinger's book was challenged for being anti-white, unacceptable, and obscene. It was challenged for language, sexual references, and centering on negative activity. The book was challenged for being blasphemous and undermining morality. At least one teacher was fired for assigning the book to an eleventh grade English class. This particular Tulsa teacher was later reinstated, but the book was not used in the school. The book has been removed from many reading lists and school libraries over the years.
The Grapes of Wrath, by John Steinbeck has also been challenged, banned, and burned. Vulgar words, the portrayal of a former minister who recounts how he took advantage of a young woman, being full of filth, and using the names of God and Jesus in vain are all given as reasons for these many challenges.
The Lord of the Flies, by William Golding has been challenged across the US over a period of decades. In 1974, it was challenged in a Texas school district. In 1981 it was challenged at high schools in South Dakota and in North Carolina. 1983 brought on a challenge in an Arizona high school. The book was challenged again in Texas in 1984. In Toronto a committee of the Canada Board of Education ruled that the book was racist and denigrated blacks in 1988. In 1992, the book was challenged in Iowa schools. In 2000, the book was challenged as a title on a ninth grade accelerated English reading list.
If you're interested in learning about more challenges of these American classics, ALA's page on banned and challenged books can tell you all about it.