There are lots of great sources available to read free fiction books online. Many popular websites such as Project Gutenberg, ManyBooks.net and Open Library offer books that are in the public domain, making them free for anyone to read. Project Gutenberg alone has over 60,000 titles available, so if you love to read and don't mind an occasional classic, it's an excellent choice.
Additionally, you can find a number of authors who provide their works for free directly from their websites. For example, J.K. Rowling, author of the Harry Potter books, makes the first book, Harry Potter and the Philosopher's Stone, available for free online. You can also find many indie authors and debut novelists who provide their works for free as a way to introduce themselves to their readers. Websites like Free-eBooks.net are good sources for discovering these kinds of authors.
Another excellent source for reading free books is your local library. Many libraries now have an online catalog where you can access free e-books and audio books, with some even offering the ability to check out physical books directly from your computer. Finally, some books may be released as free promotional e-books on Amazon, so be sure to take a look there before you decide to buy a book.