Here are a number of websites that offer free access to books that are in the public domain. This means that the copyrights have expired on these books and they are available for free (in text, or in some cases mp3 audio format).

Bibliomania --
http://www.bibliomania.com/bibliomania-static/index.html
Public domain works in fiction, drama, poetry, short stories and articles can be found here.

Full Text --
http://www.fullbooks.com/
This site contains thousands of full text free books.

Project Gutenberg --
http://www.gutenberg.org/wiki/Main_Page
There are over 20,000 free books in the Project Gutenberg Online Book Catalog. A grand total of over 100,000 titles is available at Project Gutenberg Partners, Affiliates and Resources (linked off of this website).

Audio Files (free, public domain)

Librovox
http://librivox.org/
This is a simple site to navigate and understand. LibriVox audiobooks are free. You may use them for whatever purpose you like. “Acoustical liberation of books in the public domain” is their slogan.

iBiblio
http://ibiblio.org/
This is a complex website to navigate and understand. It is home to one of the largest "collections of collections" on the Internet, ibiblio.org is a conservancy of freely available information, including software, music, literature, art, history, science, politics, and cultural studies. ibiblio.org is a collaboration of the School of Information and Library Science and the School of Journalism and Mass Communication at The University of North Carolina - Chapel Hill.

Internet Archive
http://www.archive.org/index.php
Text, audio, and video are all available on the Internet Archive, a digital library of Internet sites and other cultural artifacts in digital form.