Librivox Audibooks is for free audiobooks from librivox.com. Public domain books read by volunteers.
I don't know of any audibook app for Nook.
Yes, just recently some company has started selling audiobooks for Nook as Apps.
However, I don't know of any way to get audiobooks DIRECTLY on Nook from the Nook Store.
You can check audiobooks out through your public library with the free Overdrive app directly. Or you can also burn audiobook cd's to your computer and sideload them. The problem with the Nook is that audiobooks can take up alot of space and they would quickly consume your internal memory, such as movies would. I do agree there should be more streaming options however if you are near a wifi source. I wish there was a Nook equivalent of Audible. Libri Vox is a great app however. Unfortunately the Nook mp3 player is a crude way to get them read to you.
LibriVox Audio Books is also free at Google Play and is compatible with the NOOK. (I recommend consolidating app sources, so one's apps are easy to keep track of and can easily be re-installed in bulk, if the need arises).
OverDrive is not limited to media borrowed from libraries; in fact, its use is a prerequisite for downloading the free weekly audiobooks at YA Sync. YA Sync's audiobooks sound on the NOOK, and sound even better through earbuds/headphones. And I like OverDrive's bookmarking and progress-monitoring capabilities. On the other hand, since audiobooks are storage/memory hogs (as TriscuitCracker pointed out), and because OverDrive lacks shelving capabilties, and the NOOKs' battery life is nothing to write home about, I download duplicate audiobooks to my hard drive and I keep copies in my online user libraries and in cloud storage .
I use Audible for their proprietary books.
I'm downloading Downpour this weekend from Google Play. (Downpour's audiobooks download as zipped files, which are easy to manage on a computer, but I hope will prove easier to handle on the NOOK via the app. FYI, Downpour offers a monthly free ebook to all registrants).
A number of sites stream audiobooks online; SFFAudio.com's Online Audio page provides some examples. You can find others (as well as snag freebies/deals and read reviews of various audiobook players, content sources, and developments) by searching "audiobook" at Goodreads, Librarything, this site, Wikipedia, and the Internet in general.