Prior to the unveiling of Books.app, a book reader for the iPhone, I’d begun working on my own design. I figured the iPhone would be fairly comfortable for extended reading due to the bright display and high pixel density (which allows it to render text closer to print quality). Thanks to Chris Messina for the Keynote template with basic iPhone images he posted.
Book List
The screen you initially see after pressing the Books app icon on the Home screen:

Pressing Title switches the sorting method:

Searching
Pressing Search on the bottom button row triggers a sliding transition; the navigation buttons are replaced by a search field and Search button. The keyboard appears below.


Pressing Books returns to the list with the last active sort in effect.
Table of Contents
Nothing too special…

Book Info
Additional book details such as the original publisher and publication date. I haven’t settled on exactly what metadata should be displayed here.

Pressing the cover overlays a large version. The two-fingered spread/pinch gesture could zoom in and out.

Index
Assuming an index is embedded in the book file (or automagically generated), this would be an alternative to Search.

Pressing on a index entry displays excerpts of sentences containing the phrase in order of appearance. Pressing one of these navigates to the page.

The Book
The page structure of the physical book should be retained, but a continuous scrolling interface sounds better to me than using paging. Pages are an implementation detail (unless you are reading scrolls). The pinch/spread gesture could be used here to decrease and increase the text size, automatically reflowing the text (minding widows and orphans!). Pressing on illustrations would either overlay them similar to the cover in the Info view or open them on their own screen. If the illustration has a title and caption, a separate screen with a Go Back-type button would probably be preferable.

The zipped Keynote ‘08 file has links set up to give some idea as to the flow. Keynote’s animation tools have improved, but they are not yet to the point where I can comfortably create the transition animations that I have in mind for a book reader.
Yes, there would be a Cover Flow view when in landscape orientation. You can mock that up with your imagination. No, I do not have an iPhone. I hate phones, but I do like books.
How about an SDK, Apple?