Audible for Android
This is a popular app for people that want to use audiobooks.
https://play.google.com/store/apps/details?id=com.audible.application
Website: http://www.audible.com/
https://itunes.apple.com/us/app/audiobooks-from-audible/id379693831?mt=8
Smart AudioBook Player
This app gets a good rating.
https://play.google.com/store/apps/details?id=ak.alizandro.smartaudiobookplayer
LibriVox Audio Books Free
This app has a ton of free audiobooks.
https://play.google.com/store/apps/details?id=app.librivox.android&hl=en_US