The internet is overflowing with nearly as many free audiobooks as ebooks. There are dozens if not hundreds of sites with free audiobooks, and I have pulled together a short list of 12 sites where you can find a broad selection.
Project Gutenberg is best known for being the first website to offer free public domain ebooks, but they also have audibooks for you to download. The selection is drawn from a variety of sites, including Librivox, AudiobooksForFree, and LiteralSystems.org.
This is not your father's audiobook site. Podiobooks offers serialized audiobooks which are distributed via RSS, much like a podcast. You can subscribe with your favorite feed reader or podcast app (or at least it works for me).
The audiobooks are free, but donations are gratefully accepted.
LibriVox is a non-commercial, community-supported, ad-free site which audiobook recordings from public domain titles released by Project Gutenberg which have been read, recorded, and released for the public’s listening pleasure.
The audiobooks are created by the public, and you too can volunteer to read a story. Or you can just download from LibriVox’s acoustical library of good books.
This site stands out from the other free audiobook sites because it is the one site that focuses on audiobooks for kids, offering popular titles such as Little Red Riding Hood. It also produces original content, which comes with transcribed versions of the story.
The IA is out to backup everything, and that includes audiobooks. The site has a library of audiobooks and poetry readings from a variety of sources, including the Naropa Poetics Audio Archive, LibriVox, Project Gutenberg, Maria Lectrix, Internet Archive users, and more.
If you look elsewhere on the site you might also find audiobooks uploaded by users, but I would be careful about downloading those; at least some of the user uploads are pirated copies.
This site is one of the better gateway websites for educational and cultural media (video, text, audio, and more. Open Culture aggregates content from all over the internet, and it has a decent collection of audiobooks that you can stream or download in a variety of audio formats for later consumption. The audiobooks are listed alphabetically by the author’s last name, and are organized by genre (fiction and literature, nonfiction, poetry, etc).
As you can tell from the name, LOL is focused on educational audiobooks. This site has a collection of more than 10,000 educational and inspirational audiobooks, only some of which is free. A lot of the free content is sourced elsewhere, including other sites on this list like LibriVox, but this site's clean look and good organization might make it worth checking first.
If you're not sure what books you're looking for, just page through the listings. Hovering your mouse over the book title pops up a summary of what the story is about and offers you the opportunity to play a sample. If you find it interesting, click the title and you can download or stream the audiobook and (sometimes) read the ebook.
Lit2Go is a free online collection of stories and poems in Mp3 (audiobook) format. You can easily search for audio book titles here by genre, author or collection, and they even grade a book’s readability for your children by Flesch-Kincaid grade levels. An abstract, citation, playing time, and word count are given for each of the passages. Many of the passages also have a related reading strategy identified.
I think there aren't enough fantasy, horror, and SF podcasts in the world, even with the trio mentioned above. These 3 podcasts are free to listen, and they feature original work from authors who are paid for their contributions.