Other than books out of copyright, I don't know of any totally free e-book libraries.
Quite a few U.S. libraries (public or university) will allow non-residents to be a member for an annual fee, including access to their e-books. For instance, the Free Library of Philadelphia charges $50/year for non-residents. There are also several commercial e-book lending libraries--Amazon has one, another is Oysterbooks.com, and a third is Scribd.com (don't know if there are geographical restrictions on any of this). I have enough ebook access through my local library that I don't need them, but if I were somewhere with a limited supply of ebooks, I would definitely consider them.