
Ok. There are a ton of lists on book and reading iPhone apps out there. Too many, in fact.
Instead, I’m going to try a different and hopefully more approach: how can you find iPhone reading apps you want?
As good a place to start as any is the Top 20 Free Book Apps, courtesy of eBookNewser. The list includes some of the more recognizable ones (iBooks, Kindle, Nook, Google Books), as well as a somewhat eclectic mix of other book-themed apps.
(This brings to mind another issue for me worth thinking about — the vagueness of ebooks and book-related apps. But I’ll save that discussion for another future discussion).
A great place to look, when thinking about how to decide what reading apps are for you is a very good guide from MacWorld: “The iPhone e-book readers’ guide.” Among some of the most important things to consider —

“A reader should be helpful, resourceful and fully networked. Looking for a particular section, passage, phrase or word in an e-book? You should be able to open the search engine and tap away. Don’t know what a word means? You should be able to look it up without leaving the app. You should also be able to bookmark the definition in the text for future reference. Ideally, an app would either have an excellent built-in dictionary and thesaurus or link to a dictionary you might already have installed on your device.
If you are compulsive highlighter, the app should let you highlight text with a tap and a stroke of a finger. Prefer to underline instead? Then the app should let you opt for that. The app should let you annotate the text and bookmark as many pages as you like. You should also be able to link directly to passages and references in other works, regardless of whether you own the e-book or even if you do and it’s stored on another computer.”
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All that being said, I think the praise for the Stanza app is well-deserved, for all of the different things it does, and does well. And the desktop program comes in handy for converting to ePub and putting ebooks on your iPhone.

Thanks to that MacWorld guide, I had a look at the iFlow reader, which is another good free option.
However, an article of interest, CNET: “As iFlow Reader app closes, harsh words for Apple” with some background information on the effects of the new “agency model” of ebook sales on iTunes.
And finally, an interesting observation: “Apps are 15 times more popular than ebooks” (along with a helpful comparison, in chart form) and this historical perspective: “Books are a 400 year old medium. Songs only 100 years old and apps a mere 10. “
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[Update: I couldn’t find Fictionwise’s eReader app in the App Store, which I am assuming is a result of this, per TeleRead, “Fictionwise acquired by Barnes & Noble for $15.7 million in cash”