Rebecca Martin and Reginald Bush
Well, Christopher Marlowe for one. He wrote "Tamberlaine", "The Jew of Malta", and "Dr Faustus", before Shakespeare came along. There was also Sir Walter Raleigh, Robert de Vere, Earl of Oxford, and the one they all plump for, Francis Bacon. Others crop up, whenever anybody gets an idea, but the main contention revolves around the fact that Shakespeare never went to university, and so never had the classical education for such playwrighting that he was able to produce. In fact, he did have an excellent education, at the King's School in Stratford, being introduced to Latin at the age of nine, which he read and memorized every day until the age of fourteen, when his father, under straitened circumstance, was forced to pull him out of school. He then went on to marry, and then disappear for 8 years, until surfacing in the Earl of Leicester's Men, an acting troupe.