In what may be the earliest recorded "Your Mom" joke, Chiron confronts Aaron, his mother's lover, about the affair.  Aaron's response ends the debate (Not really. It's Shakespeare.)

A MIDSUMMER NIGHT'S DREAM, Act 3, Scene 1

THE TRAGEDY OF HAMLET, PRINCE OF DENMARK, Act 5, Scene 2

 Chrion: Thou hast undone our mother. Aaron: Villain, I have done thy mother.

"To die" was an Elizabethan euphemism for that very special feeling.   

THE TRAGEDY OF HAMLET, PRINCE OF DENMARK, Act 5, Scene 4

Benedick: I will live in thy heart, die in thy lap, and be buried in thine eyes.

Okay, okay. The word "cock" didn't come into its current slang meaning until a few decades after Shakespeare's death (also on April 23). So, this is probably not an intentional pun. But come on! 

Pistol: Pistol's cock is up, And flashing fire will follow.

As fate would have it, this middling pun comes from Hamlet, Act 2, scene 2 when Prince Hamlet asks Guildenstern and Rosencrantz how they are doing.

Hamlet: Then you live about her waist, or in the middle of her favors? Guildenstern: Faith, her privates we. Hamlet: In the secret parts of Fortune?

Sometimes, the "dirtyness" of a pun all comes down to how you say a word. Such as in Twelfth Night when Malvolio receives a letter that he thinks is from his boss, Olivia.  Use the casual pronunciation of "and" and... it gets down to the point.

Malvolio: By my life, this is my lady's hand these be her very C's, her U's and her T's and thus makes she her great P's.

The Beast with Two Backs always wants moor, moor, moor! 

Iago: I am one, sir, that comes to tell you your daughter and the Moor are now making the beast with two backs.

Did we mention that the Wall is played by an actor in this play within the play, A Midsummer Night's Dream? 

A MIDSUMMER NIGHT'S DREAM, Act 5, Scene 1

Pyromas: O kiss me through the hole of this vile wall! Thisbe: I kiss the wall's hole, not your lips at all.

Okay, this one has a long windup: Sir Andrew asks Sir Belch if he likes his hair.  Belch says it resembles a woman spinning yarn, but it's a double entendre essentially saying that Belch hopes Andrew contracts syphilis, a disease that causes hair loss. 

Sir Andrew: But it becomes me well enough, does ’t not? Sir Toby Belch Excellent: It hangs like flax on a distaff; and I hope to see a housewife take thee between her legs and spin it off.

Graze on my lips, and if those hills be dry Stray lower, where the pleasant fountains lie.

How many dirty jokes/puns are in the following line? Juliet: O happy dagger! This is thy sheath! There rust and let me die.

Malvolio: Some are born great, some achieve greatness, and some have greatness thrust upon ‘em. 

William Shakespeare is widely regarded as one of the greatest writers of all time. However, dirty jokes and risque humor abound in many of his most iconic plays.  See if you can name the plays that feature some of The Bard's most scandalous lines.