From 1990 - 1992, challenged in schools and public libraries:

James and the Giant Peach, Roald Dahl: poor portrayal of authority figures (aunts)

In the Night Kitchen, Maurice Sendak: nudity

The Adventures of Huckleberry Finn, Mark Twain: use of the word "nigger"

Bridge to Terabithia, Katherine Paterson; A Wrinkle in Time, Madeleine L'Engle; Blubber, Judy Blume; How to Eat Fried Worms, Thomas Rockwell...

The Crucible, Arthur Miller: challenged because it contains "sick words from the mouths of demon-possessed people", 1982

Where the Sidewalk Ends, Shel Silverstein: banned in Minot, ND because it undermines parental, school and religious authority, 1986

Death of a Salesman, Arthur Miller: banned in French Lick, IN for profanity, 1981

The Diary of a Young Girl, Anne Frank: challenged in Wise County, VA for "sexually offensive passages", 1982

Slaughterhouse-Five, Kurt Vonnegut, Jr.: burned in Lakeland, FL, 1982

Harriet the Spy, Louise Fitzhugh: challenged in Xenia, OH, because it "teaches children to lie, spy, back-talk and curse," 1983.

My sources are quite old, but I hope knifegirl's above examples prove that this still goes on in this day and age.