Shakespeare is the a master of this. For all the high-brow main story, he was always certain to put in plenty of lower-class pleasing vulgarities throughout all of his plays.
Hamlet contains the following exchange during Act III Scene II:
Hamlet: Lady, shall I lie in your lap? Ophelia: No, my lord. Hamlet: I mean, my head upon your lap? Ophelia: Ay, my lord. Hamlet: Do you think I meant country matters?
The lines immediately following that show off a very popular euphemism at the time.
Ophelia: I think nothing, my lord. Hamlet: That's a fair thought to lie between maids' legs. Ophelia: What is, my lord? Hamlet: Nothing.
At one point, Hamlet refers to Ophelia as being "fine kissing carrion" in front of her own father. He doesn't pick up on it, also making it an in-universe example.
"The king is a thing" - or in plain English, "the king is a dick".
The title of Much Ado About Nothing takes on a very different meaning once you realize that "nothing" was slang for female genitalia in Shakespeare's time.
The title character in Richard III uses this to have some fun with the hapless Brackenbury, concerning the king's mistress, Jane Shore:
GLOUCESTER:We say that Shore's wife hath a pretty foot, A cherry lip, a bonny eye, a passing pleasing tongue; And that the queen's kindred are made gentle-folks: How say you sir? Can you deny all this? BRACKENBURY: With this, my lord, myself have nought to do. GLOUCESTER: Naught to do with mistress Shore! I tell thee, fellow, He that doth naught with her, excepting one, Were best he do it secretly, alone. BRACKENBURY: What one, my lord? GLOUCESTER: Her husband, knave! Wouldst thou betray me?
Then again, with as many sexual slang terms as there were in Shakespeare's era, some say it's effectively impossible to speak a decently-sized sentence of modern English without saying at least three vulgar euphemisms.
How about a child Juliet falling and bumping her head, whereas if she were an adult, she would have known to fall on her back?
In Shakespeare's time, "to die" was an accepted entendre for "to have an orgasm" (based off of the French term la petite mort). Now go back and re-read Juliet's impassioned speech to her mother where she states that her dearest desire is to "behold Romeo dead" and realize what she's really hoping for.
Actually, this doesn't have to be taken in the wrong sense. Shakespeare's theater, The Globe, actually had three uses, as back in his time theaters were not allowed to be just theaters. On side of The Globe was a bear-baiting ring, where men would bet on how many dogs would be killed before the bear was fallen. The other side was a cock-fighting ring. So, this could also be a breaking the fourth wall at his audience about the Globe.
Katherine's French dialogue is pretty ribald.
Of course, Shakespeare didn't really have a radar to get crap past. Many shows were openly bawdy.
Plays did have to be approved and licensed by the Master of Revels, but Elizabethan censors were far more concerned with politics and religion than with sex. But while Shakespeare did have a radar to get crap past, it wasn't the same radar, and all of these sexual innuendos probably aren't really examples of getting crap past it..except for the modern productions which do have to slide these past.
Mostly political, which is why his "histories" have little to do with actual history.
More religious than political, actually. "The bawdy hand of the dial is upon the prick of noon" and "country matters" were perfectly acceptable, while "gadzooks", "zounds", and "'slids" were forbidden. ("Gadzooks" - God's hooks, or the nails of the Cross; "Zounds" - God's wounds; "'slids" - God's eyelids.)
By the time King Lear came out, Elizabethan theater forbid the use of God's name on the stage. And yet, Shakespeare managed to put in a lot of religious themes in the play, to the point of even paraphrasing Scripture. (I.e. "O dear father, it's thy business that I go about" paraphrases "I must be about my father's business.")
Not to mention Mercutio's little story in Romeo and Juliet.
And then there's Malvolio in Twelfth Night when he looks over the Countess's letter and exults her handwriting, how "these be her very Cs, her Us, and her Ts, and thus she makes her great Ps."
When performed at my high school, our director famously told our Malvolio for about half of his lines, "Insert appropriate inappropriate gesture here."
And then there's Helena's line "I am your spaniel, Demetrius, and the more you beat me the more I will fawn on you." I have a hard time coming up with a way of interpreting that that doesn't involve both fursuits and chains...
How about in Act I of As You Like It, when Celia mentions her and Rosalind having "slept together"? It may seem like an Accidental Innuendo, but given that this connotation of "sleeping" has been around for some time, and given Shakespeare's sense of humor in his comedies ... it's certainly possible he was joking that Celia and Rosalind knew each other that well.
Even Richard II — oft reputed as one of Shakespeare's chastest plays — has a little bawdy humor, not exactly buried but seemingly innocent enough to make the reader fear they have a dirty mind. ("Dangling apricocks" in the garden scene, in a scene rife with imagery regarding Richard's parasitic favorites.)
Probably the current king of this in American musical theater goes to the Broadway Production of Billy Elliot. At the 2009 Tony Awards, the selection they showed from the show (which was amazing, by the way) featured several instances of Billy making an obscene hand gesture. To Americans, it looks like he's holding out the number two a lot with his hand - but it's the British equivalent of an extended middle finger. But because that same gesture is so meaningless to Americans, the censor let a ten-year-old boy flip the bird repeatedly on national TV in Prime Time. Pretty audacious.
In Thirteen, During the song "Getting Ready" Lucy and Kendra share an exchange where Lucy tells Kendra she shouldn't french kiss Brett because she's a good girl. But there are moments where it doesn't sound like they're talking about kissing
And then there's this little gem...
Kendra: My mom says that pretending that you like it prepares you for marriage.
One actor in the production mentioned that changing the words "The Tongue" to "The Sex" every time it comes up is all that would be needed to change the show to 19: The Musical.He's totally right.
The blocking for "Music of the Night" in The Phantom of the Opera contains a moment where Christine gets really close to the Phantom, then darts away suddenly. While this could easily be interpreted as a result of her shyness and uncertainty, at least one member of the creative team (choreographer Gillian Lynne, IIRC) has claimed Christine was startled by brushing against the Phantom's, er, non-musical organ.
The lyrics themselves are this trope. It's easy to tell that when he's singing about all the things his music will do to Christine, he's really referring to himself.
An earlier draft of the song (which was featured in a preview staging of the first act) was even worse, with lines like "Measure after measure/An instrument of pleasure." Try singing that with a straight face.
There's also the vague possibility that he rapes her after she faints at the conclusion of "Music of the Night".
Fame: The Musical - to the point that, when buying the performance rights, the publishing company has a list of lines and even A SONG that can be cut if it's too blatant for the group performing it.
One dedicated fan compiled a list of all the train-related sexual references in Starlight Express. (The provided link automatically redirects to the main page, but the list is easily identifiable under the "Humour" section of "Fan Activity.")
Doesn't help when many of the cast members (and the Maguire himself) have said that if things had gone differently, Elphaba and Glinda would have fallen in love.
There's also the straight love duet, which has lines like "I'll wake up my body / and make up for lost time," and a seductive, "For the first time, I feel... wicked." They never go out and say "Elphaba and Fiyero slept together," but it's subtly blatant. ...If that makes any sense.
At one point, Count Zelinsky and Lady Croom are in a piano room offstage. Pleasant piano music is heard, followed by some heavy pounding on the keys, and Lady Croom comes onstage giggling and looking rather flustered. Septimus has to stop himself from asking if she just had sex on the piano.
A drunk Bernard announces to everyone at the end of the play that he and Chloe slept together.
Thomasina invites Septimus up to her room at the end of the play for some candle-lit fun. Unfortunately, he never shows, and the candle falls over and burns down the house, killing Thomasina.
During "Light My Candle" in RENT, Mimi spills hot wax on her hand, and coos "I like it between my—" Roger suggests "fingers," but it sounds like she was going somewhere entirely different... (On the final Broadway performance DVD Mimi lifts her leg suggestively on the line, making the Last-Second Word Swap even more obvious.)
Aida: After bringing the captive Aida to his room, Radames removes his shirt, asking her "Do you know what's going to happen now?" Her fearful reaction indicates that she thinks he's about to force himself on her. Instead, he orders her to wash his back, something that essentially symbolizes exactly that.
Anything Goes is the KING of this trope, especially the title song, which mentions orgies, strippers, jigolos, whores, prostitutes, OLD prostitutes, molestation, nudist parties, divorce, and make-up sex.
And this exchange from Moonface and Bonnie:
Moon: Do you suppose you could get me a sailor suit?
Bonnie: Sure! I can get you a sailor suit, he's still asleep!
Under Milk Wood by Dylan Thomas is set in the fictional village of Llareggub (pronounced Khlar - regg - ib). This looks like a real Welsh place name to the untrained eye, but try reading it backwards ...
Iolanthe: (to Strephon) When all is drear and dark/And all is drear and ark/If thou shouldst need an ark/I'll give thee one.
Phyllis: (to Lord Tolloller, hiding nearby) What was that?
Lord Tolloller: I heard the minx remark/She'd meet him after dark/Inside St. James's Park/And give him one!
1776, the musical about the Declaration of Independence, has several double and single entendres:
Lee: I'll just stop off in Stratford long enough to refresh the missus...
Or this one:
Jefferson(VA): And tonight, I'm leaving for home. Hancock(Pres): On business? Jefferson(VA): Family business. Hopkins(RI): Give'r a flourish for me, young feller!
And then these lyrics from "But, Mr. Adams":
Adams: Mr. Jefferson — dear Mr. Jefferson — I'm only forty-one, I still have my virility, And I can romp through Cupid's grove with great agility, But life is more than sexual combustibility! Glee Club: BUSTABILITY! BUSTABILITY! COM-BUST-A-BIL-A— [insert Big "Shut Up!" from Adams]