There are a hard-core group of conspiracy theorists who continue to insist that William Shakespeare was somehow not the actual author of the plays and poems that are attributed to him. In an attempt to stop the madness, Tom Reedy and David Kathman have created the most extensive list of evidence I've seen. Here's the conclusion, but reading the actual list of evidence is fascinating:
How do we know that Shakespeare wrote Shakespeare? We know because the historical record tells us so, strongly and unequivocally. The historical evidence demonstrates that one and the same man, William Shakespeare of Stratford-upon-Avon, was William Shakespeare the player, William Shakespeare the Globe-sharer, and William Shakespeare the author of the plays and poems that bear his name -- and no person of the Elizabethan and Jacobean eras ever doubted the attribution. No Elizabethan ever suggested that Shakespeare's plays and poems were written by someone else, or that Shakespeare the player was not Shakespeare the author, or that Shakespeare the Globe-sharer was not Shakespeare of Stratford. No contemporary of Shakespeare's ever suggested that the name used by the player, the Globe-sharer, or the author was a pseudonym; and none of the major alternative candidates -- not Francis Bacon, not the Earl of Oxford, not Christopher Marlowe -- had any connection with Shakespeare's acting company or with his friends and fellow actors.