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.
Nook Audiobooks is fairly straightforward. Search for books or browse via the featured titles on the opening page. Select one. Pay for it via a credit card (sorry, no Play Store or PayPal options here). Download them, play them, repeat. As with most similar apps, the books can only be played in the app itself - you won't have access to DRM-free files. The prices seem reasonable, in the scope of the often unreasonable pricing of audiobooks.
Each listing includes the narrator (a big deal for audiobook fans) and a streaming sample. Unfortunately there are no direct links for authors or narrators. Perhaps that's the "beta" nature of the app showing through. The selection seems quite good so far, considering the limitations of the smaller array of published audiobooks compared to paper books. Popular audio authors like Terry Pratchett are well-represented, but more esoteric fare is hit or miss, with the exception of political and self-help titles.