English Club reading
http://www.englishclub.com/reading/index.htm
Short Stories, quizzes, authors, etc.
Many Things American Stories
http://www.manythings.org/voa/stories/
Not only are there full texts of American short stories here, but you can listen to them or download them as MP3's.
Loud Lit
This site has short stories, novels, poetry and children's books with text and web and MP3 sound to accompany.
Repeat after Us
http://www.repeatafterus.com/index.php
Online library with a great collection of copyright-free English texts and scripted recordings. You can search by the author's last name, and even help the collection by reading some of the yet-unrecorded works!
Classic Reader
http://www.classicreader.com/browse/6/
No exercises, just lots and lots of electronic versions of literature!
ESL Monkeys Reading
http://www.eslmonkeys.com/student/storyroom/storyroom.html
Short, long and classic stories; somewhat oriented to younger learners, but has a section for students 18 and older