Overdrive Media Console available for Fire
I think OMD has been in the Appstore for at least a little while (August?) but Amazon would not let you download it to Fire, it had to be side-loaded. Perhaps in response to B&N's decision to make it available in Nook Store last week, Amazon's throwing the Fire-enable switch this week. If you don't want to sync or backup annotations, or don't like library books being added to your Kindle Library, it's a couple of steps easier than the process for borrowing a book in Kindle format. OMD gets regular updates and it is better than it used to be.
Reads ePub (including side loaded ePub)
Library finder/favorite libraries, will save your passwords