TBM Audiobooks lets you listen to audiobooks on your phone with minimal hassle. It uses folders to keep track of books and contains only the most crucial functions. Its aim is to be easy to use, clean and to simply work. For now it only works with MP3-files and may contain bugs, since it's still early in development.
The app works with Jellybean and up (4.1+).
To start using the app, simply create the folder "Audiobooks" on your phone and put the the books in subfolders, like this: