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. One of his plays, Hamlet, was written with help from the Doctor.

The Fourth Doctor claimed that Shakespeare as a boy was "very taciturn" and that he said to him, "There's no point in talking if you've got nothing to say".

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"

Via the Time-Space Visualiser, the First Doctor and his companions watched William Shakespeare in conversation with Queen Elizabeth I about Hamlet.

The Fourth Doctor claimed that he 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.

The Fourth Doctor considered Shakespeare a "charming fellow," but a "dreadful actor."

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.

The Sixth Doctor quoted Hamlet to the Master and the Rani. He called him "the Bard" and intended to meet him again.

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.

Biography from the TARDIS Data Core article, licensed under CC-BY-SA