From Scientific American:
For centuries, Shakespeare skeptics have doubted the authorship of the Stratfordian Bard's literary corpus, proffering no fewer than 50 alternative candidates, including Francis Bacon, Queen Elizabeth I, Christopher Marlowe and the leading contender among the “anti-Stratfordians,” Edward de Vere, 17th earl of Oxford. And for nearly as long, the Shakespeare skeptics have toiled in relative obscurity, holding conferences in tiny gatherings and dreaming of the day their campaign would make front-page news. On April 18, 2009, the Wall Street Journal granted their wish with a feature story on how U.S. Supreme Court Justice John Paul Stevens came to believe (and throw his judicial weight behind) the skeptics.
Stevens's argument retreads a well-worn syllogism: Shakespeare's plays are so culturally rich that they could only have been written by a noble or scholar of great learning. The historical William Shakespeare was a commoner with no more than a grammar school education. Ergo, Shakespeare could not have written Shakespeare. For example, Stevens asks, “Where are the books? You can't be a scholar of that depth and not have any books in your home. He never had any correspondence with his contemporaries, he never was shown to be present at any major event—the coronation of James or any of that stuff. I think the evidence that he was not the author is beyond a reasonable doubt.”