Aside from the Shakespeare plays listed...
"My Fair Lady" is directly based on Shaw's play Pygmalion, not the actual Greek myth itself, which I wouldn't really count as a book either.
"Oklahoma!" is based on Lynn Riggs' "Green Grow the Lilacs," which is also a play.
"The King & I" is directly based on the film "Anna and the King of Siam," with some of the dialogue exactly the same. The film in turn is based on Margaret Landon's book, so I suppose that's an indirect association.
Some are collections, like "Guys and Dolls" based on collected stories by Runyon (two in particular)... or "South Pacific" based on stories from "Tales of the South Pacific" by Michner, and "Into the Woods," based, in part, on several Grimm fairy tales.
Here are a few more others directly based on books, though:
The Wiz (based directly on the Baum book)
The Sound of Music (based on Maria Von Trapp's book)
The Color Purple
"Jaws is the Citizen Kane of movies."
blocked: logan2, Diamonds3, Hamilton22