Interestingly enough, although there are many sites that have apps for the iPhone (WordPress is one of them), I have yet to find a library app. There are many different books, and book reading apps (Kindle and B&N reader, among others) available, many of which are free (yay!) but no library app. I found that quite interesting. The idea of most apps is to allow the user to have instant or easy access to the content. I think it would be very valuable to have a 24/7 or ask your librarian app, a book finder app, a library account app, etc. I will keep looking and tell you if I do find anything, but as of right now I am still looking (and am slightly disappointed).
Apps for iPhone