In a case of works, rather than actors, existing in-universe, RENT is a 20th century adaptation of La Bohème. In the show, Roger plays a strain of music on his guitar and Mark comments that it sounds like "Musetta's Waltz"... which is from La Bohème. One wonders if the characters noticed how closely their lives reflected the opera.
Well, there IS a song called "La Vie Bohème."
Older Than Steam: In Molière's play The Imaginary Invalid, which satirizes the medicine of the era, the brother of Argan (the hypochondriac main character) asks him if he would like to see a Moliére play. Argan angrily berates Moliére for making fun of doctors.
[title of show]. A musical about writing a musical about writing a musical, the musical they're writing being [title of show]. The main characters are all played by themselves, and the musical debuted at the theater festival the characters discuss debuting the musical at. Needless to say, there is a very small window in which this musical works as well as it was intended to.
Which definitely passed by the time the play was performed by the Arizona Theatre Company.
The possibility of who plays them after the initial run was addressed in ''the [title of show] show'' episode 6.. Also, in other behind the scenes material, it can be seen that two standbys had been hired.
In Don Giovanni by composer Wolfgang Amadeus Mozart and librettist Lorenzo da Ponte, Don Giovanni and his servant Leporello divert themselves by singing snippets of opera, first an aria from Una cosa rara by Vincenzo Martini, a colleague of Mozart's who frequently collaborated with da Ponte, then one from Fra i due littiganti by Sarti, and finally Non più andrai from The Marriage of Figaro by Mozart and da Ponte, at which Leporello notes that the tune sounds very familiar. It is believed that this was part also a nod to the audience in Prague (where Don Giovanni was first performed), because in Prague unlike Vienna the Marriage had been a huge success.
Gilbert and Sullivan: Interestingly, true in some cases but not others. HMS Pinafore exists as a fictional play in The Pirates of Penzance ("whistle every tune from that infernal nonsense Pinafore), but King Paramount in Utopia Limited says that he's in touch with a certain Mikado of Japan with some interesting views on punishment.
The Show Within a Show in The Drowsy Chaperone is said to have first debuted in the Morosco Theatre. When the (real) show went to Broadway, it debuted in the Marquis Theatre, which was built on the same site as the Morosco. They even acknowledge it in the show's dialogue, making it a Mythology Gag as well.