Visit Project Gutenberg (see link in Resources), where over 40,000 free books are available in a variety of formats. You can search Project Gutenberg's database by title, author, genre, subject or keyword. You can also view a list of the most popular books of the day, week or month.
Visit the Internet Archive (see link in Resources), where "a wide range of fiction, popular books, children's books, historical texts and academic books" are available for free. The Internet Archive offers a powerful search function similar to Project Gutenberg's. You can also view the most popular downloads of last week and of all time.
Visit Amazon.com's Kindle Store (see link in Resources). Amazon may not come to mind as a source of free books, but sorting to place the lowest-priced books at the top reveals thousands of free books to choose from, both fiction and non-fiction. Use the list of categories to refine your search.
Visit Open Library (see link in Resources). The goal of Open Library is to create one "web page for every book ever published." As of August 2012, Open Library offers nearly 1.2 million free books for download.