I don't understand the appeal of audiobooks but I have friends who swear by them. Audibly is an app that'll surely make those friends of mine happy as it offers 2947 classic audiobooks catalog for free.
The app uses narrators from Librivox, and from a few quick listens, they all sound perfectly fine. Of course you won't be able to listen to the most current of books (so no Twilight, sadface) but it's still a nice selection of books that're free in the public domain: Shakespeare, Benjamin Franklin and Teddy Roosevelt autobiographies, Sherlock Holmes, sci-fi novels and a ton more. The app is easy to use too, it keeps the books in a list and lets you browse sections by swiping the top (sorta Windows Phone 7-esque, in that aspect).
The ads are sort of annoying but I'm sure you'll be able to deal with it when everything is free listening. I still don't think I'm an audiobooks guy though. [iTunes]