Since Shakespeare didn't write 'books'.. the answer is Jules Verne. Who had over 70 big screen movies and 20 tv movies based on his novels. Sir Arthur Conan Doyle has had a lot of movies based on his Sherlock Holmes character but not necessarily his books.
My favorite is Stephen King who has had 31 movies to date based on separate books/short stories (Shawshank Redemption, The Green Mile, The Shining, Stand By Me, and Apt Pupil are his best in my opinion.)