The U.S. Library of Congress' site, Read.gov/kids, has several classic children's books available to read online, including favorites, such as "Fairy Tales of the Brothers Grimm." Project Gutenberg also maintains a children's book shelf with several classic picture books for children, which includes the popular works of Beatrix Potter.
Children's Books Online has online books for pre-readers as well as early, intermediate and advanced readers. It offers audio books and books in foreign languages as well. Children's Storybooks Online offers online stories for young children, older children and young adults. Several stories include audio, so even pre-readers can enjoy these books without help from their parents.