William Shakespeare

William Shakespeare was known as the greatest poet and playwright in the history of England and one of the greatest in human history. The Doctor considered him the most "human" human that ever lived. He also had numerous encounters with the Doctor and was attracted to Martha Jones and possibly the Tenth Doctor himself. (TV: The Shakespeare Code) One of his plays, Hamlet, was written with help from the Doctor. (PROSE: The Stranger, The Writer, His Wife and the Mixed Metaphor, TV: City of Death, AUDIO: The Foe from the Future) According to the Dalek version of Earth history, he was, throughout his entire productive life, a covert Dalek agent. All of his work was in fact written by the Dalek Emperor. (COMIC: City of the Daleks)

Encounters with the Doctor
While travelling with the Sixth Doctor, Peri Brown found the original draft of an unknown play by Shakespeare, Mischief Night, in the TARDIS. (COMIC: Changes)

The Eighth Doctor and Charley Pollard met a young Will Shakespeare who had been taken out of his rightful time (1572) by Viola Learman and brought to New Britain in the early 21st century. Will Shakespeare may have learnt about his own plays from Mariah Learman's library. (AUDIO: The Time of the Daleks) The three of them briefly ended up in Asia Minor, where they encountered the Doctor's previous companion, Vicki, calling herself Cressida, and her husband Troilus. The Doctor was afraid that Will would learn too much about his future play, Troilus and Cressida, but learned that Shakespeare had not invented the story. (PROSE: Apocrypha Bipedium) Due to the traumatic nature of these and later events, his life may have been changed retroactively to explain any discrepancies. (AUDIO: Zagreus)

In 1597, the Fifth Doctor shared a drink with an older Shakespeare; he later stowed away in the TARDIS and began to attempt to influence the reign of King Richard III of England to more closely resemble the account in his play Richard III. This adventure ended with Shakespeare being killed in King Richard III's place at the Battle of Bosworth on 22 August 1485, and Richard returning to 1597 to take Shakespeare's identity and place in history. It is heavily implied that the Celestial Intervention Agency fixed the events of this story, which may explain how Shakespeare later did not recognise the Doctor. (AUDIO: The Kingmaker) The First Doctor collaborated with Shakespeare between drafts one and two of Hamlet. (PROSE: Byzantium!)

Some time in the same decade, the Ninth Doctor and Rose Tyler encountered Shakespeare. At the Doctor's request, Rose agreed to distract Shakespeare "with a hey nonny nonny." He dismissed an attempt by Shadeys to destroy the Earth as a trick-show, and did not let it interfere with his future career. The meeting between the Doctor and Shakespeare was fleeting however, and may not have made much of an impact on his life as other meetings subsequently did. (COMIC: A Groatsworth of Wit)

In 1599, the Tenth Doctor encountered Shakespeare when the witch-like Carrionites wanted the wordsmith to complete the play Love's Labour's Won to free the rest of their kind. With the help of the Doctor and Martha Jones, the three Carrionites and their sisters were banished back into the Deep Darkness. During this encounter, Shakespeare developed an attraction to the Doctor and Martha, whom he addressed as his "Dark Lady" (TV: The Shakespeare Code).

Via the Time-Space Visualiser, the First Doctor and his companions watched William Shakespeare in conversation with Queen Elizabeth I. (TV: The Chase)

Years later, the Fourth Doctor helped Shakespeare transcribe Hamlet as Shakespeare had sprained his wrist writing sonnets. The Doctor claimed that he had warned Shakespeare that Hamlet's line "to take arms against a sea of troubles" was a mixed metaphor, but Shakespeare would not listen. (TV: City of Death, PROSE: The Stranger, The Writer, His Wife and the Mixed Metaphor) He later told Leela that Shakespeare was the greatest poet in the English language "with [his] assistance." (AUDIO: The Foe from the Future)

Conversely, the Fifth Doctor later described him as a "hack" to his companions Peri Brown and Erimem. (AUDIO: The Kingmaker) However, By the time of his tenth incarnation, his opinion of Shakespeare's work had considerably improved as he spoke of it in glowing terms to Martha. (TV: The Shakespeare Code)

In 1609, Shakespeare, acting as an agent of the Crown, encountered the First Doctor, Irving Braxiatel, and Galileo Galilei in Venice, and was reunited with Christopher Marlowe, whom he thought was dead. The Doctor forcibly made Shakespeare take a retcon-like drug to erase his memory of the events that he had witnessed.

Shakespeare died in Stratford-upon-Avon in April 1616, having been poisoned on the orders of Sir Walter Raleigh who had been released from the Tower of London only five weeks earlier. Braxiatel visited the playwright on his deathbed and restored the Englishman's memories of his time in Venice. (PROSE: The Empire of Glass)

Later references
The Sixth Doctor quoted Hamlet to and the Rani. He called him "the Bard" and intended to meet him again. (TV: The Mark of the Rani)

In the 25th century, the work of Lynda LaPlante was more highly regarded than that of Shakespeare. (PROSE: The Plotters)

Personality
Shakespeare was notable for being one of the few humans who, without receiving any known sort of psychic training, was not fooled by the Doctor's psychic paper. The Doctor was very impressed by this fact and applauded him, stating it was proof that he was a genius. (TV: The Shakespeare Code)

The Ninth Doctor told Rose Tyler that, despite rumours, Shakespeare was very much heterosexual. (COMIC: A Groatsworth of Wit) In spite of this, he still flirted with the Tenth Doctor, to which the Doctor commented, acedemics just punched the air." (TV: The Shakespeare Code)

Behind the scenes

 * In The Shakespeare Code, the Tenth Doctor acts as though he's never met Shakespeare before, despite the Fourth Doctor indicating in City of Death that he knew Shakespeare well enough to help him write Hamlet. Reportedly a line of dialogue was written for the later episode to explain this, but the line was cut. The Ninth Doctor also claims in A Groatsworth of Wit that he's known Shakespeare "for ages".
 * During The Shakespeare Code there is a moment when the Doctor notices Shakespeare is flirting with him after just having done so with Martha. The Doctor says, "Come on, we can all have a good flirt later!" [in reference to them needing to stop the Carrionites]. Shakespeare responds, "Is that a promise, Doctor?" The Doctor muses, mostly to himself, "Fifty-seven academics just punched the air." This is a reference to the idea that most of Shakespeare's sonnets, including Sonnet 18, are believed by some Shakespearean academics to be addressed to a man, and there is a sizable body of scholarship on Shakespeare's sexuality.
 * The revelation in AUDIO: The Kingmaker that the original Shakespeare left his time in 1597 and was killed in 1485, only for Richard III to return to 1597 and take the prematurely deceased writer's place, has not been acknowledged or addressed by in-universe portrayals of Shakespeare post-1597.
 * According to The Brilliant Book 2012, a non-narrative REF book; in 1605, Shakespeare met Amy Pond and Rory Williams at a show of Romeo and Juliet and flirted with Amy until King James I tried to arrest them for their association with the Doctor. The book also said that in a timeline where all of history occurred at once, Shakespeare was the head writer of EastEnders.