There's a surprising lack of options when it comes to Android audiobooks. Sure, there's Audible, but its metered subscription service isn't an ideal solution for a lot of people, and other services tend to be light on content. Audiobook enthusiasts now have another alternative: Barnes & Noble. NOOK (ALL CAPS) Audiobooks is available as a free download on any Android 4.0+ device, though I'm betting that only those in the US can actually buy books.
When the time comes to shop for ebooks, Amazon's Kindle Store is one of the first online destinations that comes to mind. Likewise, Audible, a company now owned by Amazon, is an easy recommendation for audiobooks. Thus far, people who own both the ebook and audiobook versions of a novel have had to hop back and forth between mobile apps to switch between the two.
Reading a book using the Kindle app vs listening to it via Audible.
If you want to listen to an audiobook, Audible is the number one source. Though, the app was never great on Android. It wasn't terrible, but it didn't have a strong Android aesthetic and the layout was strange. With the version 1.5 update, that's a thing of the past. The app looks excellent now, and there are other improvements too.