The University of Pennsylvania has posted an online-books page that carries over 35,000 free books to read. The site is updated with new books almost daily, and books range from classics from the 1800s to titles published this year. Every subject imaginable is covered, with multiple ways to search.
Wowio is an online site that lets you choose between paying for ebook downloads or reading the exact same book online for free. There is a large number of books to choose from here, with subjects ranging from photography to modern literature. There are children's books, graphic novels, craft books and dozens of other types of books.
Project Gutenberg is the oldest and first online book site. Uploaded by volunteers, the books are all classics past their copyright dates. Many of the best literature of the Western world has been uploaded onto this site, and all of it is free to read.
Baen Books is a science fiction and fantasy site that has a different idea: give away free copies of ebooks, and perhaps readers will want to purchase copies of later works from the same authors. Whether or not you want to buy anything, you are free to read any of the hundreds of books on the Baen site, either online or by downloading them to your PC or mobile device.