Shakespeare's plays include several Shout Outs to earlier Shakespeare plays. Notably, Hamlet includes several references to Julius Caesar. At one point Polonius claims to have played Caesar on stage, almost certainly indicating that the actor who originally played Polonius had previously played Caesar in Shakespeare's version. (Like Caesar, Polonius is also stabbed to death, although in his case it's due to mistaken identity.)
Shakespeare's Troilus and Cressida quotes Marlowe's Doctor Faustus on Helen of Troy. This sounds slightly weird to a modern audience, as the line in question ("Was this the face that launched a thousand ships?") has become cliché — it's probably the most famous sentence Marlowe ever wrote.
The mirror scene in Shakespeare's Richard II could well also be a reference to that same line.
Jury: Our object all sublime We shall achieve in time, To let the melody fit the rhyme, The melody fit the rhyme. Ringmaster: This is all immaterial and irrelevant! What do you think this is — Gilbert and Sellivant?
Also done in The Pirates of Penzance, where Major General Stanley sings that he can "whistle all the airs from that infernal nonsense Pinafore", referring, of course, to Gilbert and Sullivan's previous hit, H.M.S. Pinafore. The finale originally included a direct paraphrase of H.M.S. Pinafore:
Girls: Oh, spare them! They are all noblemen who have gone wrong! Major-General: What, all noblemen? King: Yes, all noblemen! Major-General: What, all? King: Well, nearly all!
The opening/title number of In the Heights gives a shout out to Cole Porter, mentioning "Too Darn Hot" from Kiss Me Kate.
In the Heights also contains shout outs to the song "Take the A Train", the Broadway star Chita Rivera, and It's a Wonderful Life.
RENT gives a specific shout out to La Bohème, the opera it's based on, in "La Vie Boheme" when Mark remarks Roger's song sounds like "Musetta's Waltz". Roger's guitar motif is the opening phrase to "Musetta's Waltz." A more subtle reference to the same aria occurs in "Take Me or Leave Me," where Maureen's first verse (where she describes people admiring and flirting with her as she walks down the street) has the same basic theme as "Quando me n'vo." The opening number contains another riff taken directly from La Boheme.
Ironically enough, the same riff is used in Lloyd Webber's "Make Up My Heart" from Starlight Express.
Then there's "Christmas Bells," which in many ways is a Darker and Edgier riff on La Boheme's holiday street scene. Most notably, the children chasing after the toy seller Parpignol in the original become drug addicts trailing after "The Man," their supplier.
Tick Tick Boom!, another Jonathan Larson musical, is filled with shout outs to Stephen Sondheim. The biggest of these is the song "Sunday", which is an update of a song by the same name in Sunday in the Park With George.
A very subtle one from Gilbert and Sullivan's The Pirates of Penzance: "Poor Wandering One" is really, really similar to "Sempre libera" from Verdi's La traviata. Most likely intentionally, consideirng that "la traviata" means "she who has strayed," which is the subject of G&S's song....
In the original Russian version of Uncle Vanya, towards the end of Act 3, the professor announces to his assembled family members that a government inspector is coming, before launching into his speech. It is a reference to an earlier play named, funnily enough, The Government Inspector, by Nikolai Gogol.
In Act I Scene VII: Theophrast Reunadetshows up briefly only to be dismissed by Cyrano ("Who cares?"). Renaudet was homely and this affected him throughout his life (the real Cyrano seemed not so affected by this), an incident at his youth drove him to help the poor and the outcasts, highly idealistic and talented, was named the royal doctor and create La Gazzete, the first official paper of the world, and at 1632 was recognized by the King as one of finest Frenchmen. He (like Cyrano in the play) died in obscurity and poverty in 1653. The parallelism between his life and Cyrano’s character in this play were not highlighted by the English wiki article, but they were in the Spanish article: here.
Act I Scene III, Montfleury says the first lines of Phedon, a character from “La Clorise”, a real play written by Balthazar Baró, Cyrano’s contemporary playwright. It's an excersice to the reader after seeing the first three lines of the play if this is a true Shout-Out or a Take That:
Montfleury:: "Heureux qui loin des cours, dans un lieu solitaire, Se prescrit a soi-meme un exil volontaire, —-> Et qui, lorsque Zephire a souffle sur les bois. . ."
To Tito and Berenice and Cesar and Cleopatra, two of the most famous romances in history at Act I Scene V.
De Guiche(who has controlled himself—smiling):"Have you read Don Quixote?"
CYRANO: I have!
In Puccini's one-act opera Il Tabarro, the refrain to the balladeer's song of Mimi includes an instrumental quote of "Mi chiamano Mimì" from La Bohème.
The original London production of Chess had Anatoly watching television in a scene and at one point ABBA's "Money, Money, Money" can be heard, a shout out to the show's Pop Star Composers, Benny Andersson and Björn Ulvaeus of ABBA.
The 2010 UK Tour of Chess inserted a line from "Money, Money, Money" into the song "Merchandisers."
The title song of Allegro includes a short parody of "The Whiffenpoof Song":
They are smart little sheep who have lost their way. Blah! Blah! Blah!
Amaluna is loosely based on The Tempest as well as referencing other Shakespeare plays (e.g. the Romeo and Juliet-esque waterbowl falling in love scene), and the white-dressed Peacock Goddess and her black alter ego echo the White and Black Swans from Swan Lake.
In Let 'Em Eat Cake, Kruger, in his nihilistic List Song, says, "Down with pianists who play 'Nola'!" The first two bars of "Nola" are then interpolated.
In Carl Orff's opera Die Kluge, when the vagabonds talk of the power of luck, one of them says, "O Fortuna, velut luna!" This is, of course, the first line of Orff's setting of Carmina Burana.