Sources
Anarchist/Leftist Works
Another World is Possible - Small library of anarchist audiobooks on Archive.org
Audio Anarchy- MP3s of anarchist texts (Archive.org Backup)
Audible Anarchist (YT) - Anarchist texts hosted on Youtube and Soundcloud. See /f/AudibleAnarchist for more.
Free Radical Radio Audiobooks - Audiozines and snippets of Audiobooks
Leftist Theory Audiobooks (YT) - Leftist texts hosted on Youtube
Raddle's Audiobook Library - Under construction by /f/audiobooks
Raddle's Podcast Wiki - Podcast library by /f/Podcasts
Resonance Audio - Anarchist Audiobooks & Audiozines. Also hosted on their Youtube channel and site
Legal Multilanguage
Archive.org / Librivox / Project Gutenberg Audiobooks
Loyal books - 7000+ audiobooks
English Only
OpenCulture - 900 audiobooks
Lit2Go - Literature classics from a university library
Non-English
French: http://www.litteratureaudio.com/ - 6000+ audiobooks
Piracy (Use privacy software/VPN)
Audiobook Bay - huge selection
Unwelcome Guests Audiobooks - a few direct MP3 downloads
Mobile Software
Android: Voice (Audiobook Player) - Great interface and features, and of course free/GPL software.
iOS: Audiobook-Player/BookPlayer - free/GPL software
If you know additional sources/software to list, feel free to edit this yourself or post in /f/audiobooks.