OneClickdigital (formerly NetLibrary/Recorded Books) - Thousands of always available audio books, primarily adult titles. Currently available on Macs, PCs, and via an iOS (Apple) or Android app.
OverDrive - Find adult, teen, and children’s fiction, nonfiction, popular authors, current and backlist titles.
Internet Archive: Audio Books and Poetry - A collection of free audio book and poetry recordings. (Non-library site)
LibriVox - Public domain audio books recorded by volunteers, some in non-English languages. (Non-library site)
Open Culture: Free Audio Books - Public domain audio books through iTunes, Audible, and more.(Non-library site)