If you own an Apple device and want to access library ebooks on it, try the free Bluefire app now available on the App Store. It has the ability to authorize and open OverDrive files, so you can read your library books on your iPhone or iPad.
The original instructions at mobiputing.com explain the app and show several routes for getting the library book on your device.
The modified instructions at libraryjournal.com explain how to use your email account to move the appropriate file from your PC to your iThing.
Sadly, the Kindle still won’t play nice with OverDrive files and isn’t likely to change in the near future, which is probably its single biggest shortcoming compared to other devices. (The Kobo, nook, and Sony Readers all support library lending!) In other words, Bluefire won’t solve the Kindle/library problem, but at least it’s a useful solution for bookworms who happen to have iPhones and/or iPads.