DigitalBook.io lists public domain audiobooks from other sites. Some of them can be downloaded and others have to be streamed from their site.

LibriVox is a volunteer organization that records and offers for free public domain audiobooks for download. They have more than 10,000 works available.

Lit2Go is a collection of audiobooks and excerpts that are available to listen to online or through iTunesU.

Loyal Books has a large collection of classic fiction and nonfiction ebooks and audio books.  Most of their collection is from Project Gutenberg and LibriVox.

Open Culture is a website with a curated list of free audiobooks, ebooks, and videos.  They offer fiction as well as nonfiction, online courses, movies, and language-learning resources.

Storynory is a website that has free ebooks for children that they can listen to online. The stories are illustrated and the story is also published on the page, so people can read along.