The following is a non-exhaustive list of contenders:
* William Herbert (the Earl of Pembroke). Herbert is seen by many as the most likely candidate, since he was also the dedicate of the First Folio of Shakespeare's works.
* Henry Wriothesley (the Earl of Southampton). Many have argued that 'W.H.' is Southampton's initials reversed, and that he is a likely candidate as he was the dedicate of Shakespeare's poems Venus & Adonis and The Rape of Lucrece. Southampton was also known for his good looks, and has often been argued to be the 'fair youth' of the sonnets.
* Sir William Harvey, Southampton's step-father. This theory assumes that the fair youth and Mr. W.H. are separate people, and that Southampton is the fair youth. Harvey would be the "begetter" of the Sonnets in the sense that it would be he who provided them to the publisher.
* William Himself (i.e. Shakespeare). This theory was proposed by the German scholar D. Barnstorff, but has not found much support.
* A simple printing error for Shakespeare's initials, 'W.S.' or 'W. Sh'. This was suggested by Bertrand Russell in his memoirs, and also by Don Foster in "Master W.H., R.I.P." (PMLA 102, pp. 42-54) and by Jonathan Bate in The Genius of Shakespeare. Bate supports his point by reading 'onlie' as something like 'peerless', 'singular' and 'begetter' as 'maker', ie. 'writer'.
* William Hall. Hall was a printer who had been responsible for printing other work that Thorpe had published (according to this theory, the dedication is simply Thorpe's tribute to his colleague and has nothing to do with Shakespeare). This theory, started by Sir Sidney Lee in his A Life of William Shakespeare (1898), was continued by Colonel B.R. Ward in his The Mystery of Mr. W.H. (1923). Supporters of this theory point out that the full name "William Hall" appears if the word "all", immediately following the initials in the dedication, is added to them. There is also documentary evidence of one William Hall of Hackney who signed himself 'WH' three years earlier, but it is not certain that this was the same man as the printer.
* Willie Hughes. The 18th century scholar Thomas Tyrwhitt first proposed the theory that the Mr. W.H. (and the Fair Youth) was one "William Hughes", based on presumed puns on the name in the sonnets. The argument was repeated in Edmund Malone's 1790 edition of the sonnets. The most famous exposition of the theory is in Oscar Wilde's short story "The Portrait of Mr. W.H.", in which Wilde, or rather the story's narrator, describes the puns on "will" and "hues" in the sonnets, and argues that they were written to a seductive young actor named Willie Hughes who played female roles in Shakespeare's plays. There is no evidence for the existence of any such person.
* William Haughton, a contemporary dramatist.
* William Hart, Shakespeare's nephew and male heir. Hart was an actor himself and never married.