Listen to Robert Munsch read almost all of his books (audio only, no visuals). Munsch is the author of such books as 50 Below Zero, Love You Forever, and Thomas' Snowsuit.
There are actually over 500 books, now, in spite of what the illustration says. Basically, these are YouTube videos of books being read aloud, so they aren't necessarily professional, but they are all gathered together on one webpage.
About 25 picture books read online by celebrities. From The Rainbow Fish read by Ernest Borgnine to To be a Drum read by James Earl Jones.
Listen to Mem Fox, author of Koala Lou and Tough Boris, read six of her books (audio only)
Dozens of online books available for beginning readers to practice with.
National Geographic - Young Explorer has almost 50 issues of it's magazine online to read for free. Plus, they are always adding more.
Audio only for the stories on this site - the text is provided, but no illustrations.
Several Howard B Wigglebottom books are available to read, at this webpage.
18 Picture Books read by celebrities. For example, Fancy Nancy read by comedienne Rita Rudner and Excuse Me read by comedian Carrot Top.
On the Barnes and Noble website, there is a collection of 16 stories read aloud by the author or a celebrity. For example, The Kissing Hand is read aloud by the author Audrey Penn, and Green Eggs and Ham is read aloud by celebrity Rachel Ray.