In addition to all the free e-books you can enjoy from the library, there are several web sites that provide access to out of copyright or open source e-books and you can access them any time without your library card.
Project Gutenberg provides access to over 45,000 free e-books that you can download for offline reading in either ePUB or Kindle formats, or simple read online through any internet browser. They've digitized all the books themselves, including titles from Jane Austen, Mark Twain, William Shakespeare and many many more.
The Internet Archive and Open Library offers over 6,000,000 public domain e-books, including over 500,000 eBooks for users with print disabilities. You first have to register with the Open Library web site, but then you can "borrow" and read as many e-books as you like. Featured authors include Charles Dickens, F. Scott Fitzgerald and many modern authors, too!
Open Culture features access to 600+ e-books and so much more, including audiobooks, free online courses and movies.
HathiTrust is a partnership of academic and research institutions that offers millions of titles digitized from research libraries around the world. You can browse through the collection and read e-books in both desktop and mobile browsers.
Google Books allows for full text searching and browsing through millions of books and magazines that have been digitized by Google.
Books Should Be Free has e-books and audiobooks from the public domain in English and many other languages. Titles work on Android, iOS, and Kindle.
Free e-books in other languages can be found at these sites:
The International Children's Digital Library contains nearly 5,000 children's book titles in 59 different languages. It also features a kid-friendly search interface, with facets like book cover color and what type of characters the book features.
For Spanish titles, try El Libro Total, which features Spanish classics and Latin American works.
For free French downloadable audiobooks, look no further than AudioCite.
VietMessenger features Vietnamese ebooks from many genres. Simply register with the web site and download away.