As TUAW's own Robert Palmer noted a few weeks ago, there are over 20 Bible applications available for iPhone. Some require an Internet connection to query an online Bible database, while others store the text on the device.
HANDiBIBLE (formerly Pocket Bible) is one of the latter apps, and is now available in the App Store (iTunes link). The developer, Jerry Beers, made an easily accessible (US$4.99) and usable Bible application and realizes that version 1.0 is just the start -- he welcomes feature requests.
At the present time, HANDiBIBLE provides an easy-to-use interface to a King James Version of both the Old and New Testaments. Readers pick which Testament they wish to read and a list of all of the books appears. Pick the book by tapping on it, and a set of scroll wheels appears which are used to set the Chapter and Verse. Tap go, and you're reading.
Since the developer has asked for feature requests, I'd suggest a word search mechanism and a New King James Version translation for readability. Despite these suggestions, HANDiBIBLE is a well-done and affordable Bible application for iPhone.