AudioBooksForFree.com is a great website containing a library of free audiobooks from a large variety of authors, from modern literature to classics. Filters and search engines within the page can make searching for audiobooks easy.
AudioBooksForFree is a website usable for all ages, and even contains a children's book section. The Privacy Policy says that the site collects as little information as possible from visitors to the site so that it is a safe online place to send students to find resources.
