The American Library Association (ALA) keeps statistics on and creates lists of challenged books and authors. Books for children and young adults often comprise the majority of these lists.
The following children's and YA books are on the list of the 10 Most Frequent Challenged Books of 2012:
Staley Library's juvenile collection also contains many of the children's and YA titles on ALA's 100 Most Frequently Challenged Books of 2000-2009, 100 Most Frequently Challenged Books of 1990-1999, and Banned and Challenged Classics. Take a look at the list and do a search by "Title" search in our Online Catalog for the book you're interested in.
For more information and resources from ALA on challenged and banned books, please see their website on the subject (especially useful is the link challenge support).
or take a look at some Staley Library books on this subject:
Other resources useful in researching banned books include these databases (try searching by book title (and/or author's name) and include the words "challenged," "banned," or "controversy" in your search):
Also, try looking for the author's official website or an interview with the author online. Many will often comment when their books are banned.
Other useful websites for book challenges: