In the U.S., this week (September 27 – October 3) is Banned Books Week. It is a national event founded in 1982 to raise awareness to the fact that people are still trying to ban books.
The American Library Association states, “By focusing on efforts across the country to remove or restrict access to books, Banned Books Week draws national attention to the harms of censorship.” On its website, the ALA has lists of the most frequently challenged books (http://www.ala.org/bbooks/frequentlychallengedbooks/top10). It is certainly a worthwhile site to browse. Some of the books on those lists may surprise you.
An article appeared in Slate magazine arguing that Banned Books Week is an anachronism. The author states that the event is fear-mongering about a non-existent wave of censorship: http://www.slate.com/articles/arts/culturebox/2015/09/banned_books_week_no_one_bans_books_anymore_and_censorship_of_books_is_incredibly.html. BookRiot posted a response which argues that “When books are challenged, even when the result is not a full ban, nobody wins” (http://bookriot.com/2015/09/29/hey-slate-banned-books-week-isnt-crock/). Read both articles and form your own opinion.