This past weekend I downloaded an iPhone app that I love. It is the KJV Bible Audiobook. I am unfamiliar with the developer (iTourSoftware) or the church affiliation, but the app is first rate. It is much more than an audiobook. It is really a KJV Bible application with the option to listen. The user interface, search function, bookmarks and notes features are simple to use and more than adequate for their purpose.
This app won't replace a Bible study app like Logos, but the audio function definitely makes this app worth having. I have downloaded, tried and erased several iPhone Bible apps, but this one is a keeper.
And best of all it's free. You can donate, of course, and the proceeds support a good cause as best I can tell. I haven't found where the app is available for other smartphones, so sorry non-iPhone users.
Note: since the app contains the entire audio KJV Bible, it will take a while to download on wifi (it took me almost an hour), or you can transfer from iTunes. But, the app loads and runs fast and I have not noticed any side effects from the file size. Enjoy!