Encyclopedia Mythica Folktales - Folktales from around the world including Native American, Central American, European and Asian. 

Aesop's Fables - Brief versions of over 655 fables.

Folklore and Mythology Electronic Texts - Full text online folklore and mythology edited and/or translated by D. L. Ashliman University of Pittsburgh. Conveniently sorted by topic, such as "frog prince tales", or "Cinderella." Some topics may not be suitable for elementary students. 

Grimm's Fairy Tales - 209 tales, not illustrated.  Or sample the original versions at National Geographic.com
         
Hans Christian Andersen: Fairy Tales and Stories - 84 stories in chronological order.

Mother Goose - An alphabetical index of Mother Goose rhymes. 

Tales of Wonder - Folk and fairy tales from around the world.  Maintained by Richard Darsie.