The Stateroom Sketch

A character has just moved into a small room the size of a closet. For added hilarity, it may even be an actual closet. This person barely has room to stand up in, so what's the first thing that happens? He gets visitors. Lots and lots of visitors.

Originally done by the Marx Brothers in A Night at the Opera: Groucho boards a ship and finds he has been booked into a stateroom so tiny that it barely holds him and his luggage. Inside his luggage, however, he finds stowaways Harpo, Chico and the movie's leading man. Then in come the maid, the electrician, some waiters with food, a girl looking for her aunt... It often climaxes with one last person opening the door and everyone tumbles out.

All other versions of this gag are most likely an homage to the original, which was developed by Buster Keaton who reworked a similar sequence from his film, The Cameraman.

Compare with Clown Car Base.

Examples of The Stateroom Sketch include:

Film

A Night at the Opera, of course.
Done in Brain Donors with Volare's dressing room. Appropriate, given that the movie is a remake of A Night at the Opera.

Literature

In Curse of the Wolfgirl fashion designer Thrix is preparing for a date and is visited by almost every non-villain character.
The children's book The Mitten is about a mole who finds a lost mitten and climbs in to keep warm, followed by a rabbit, then a hedgehog, etc etc...

Live Action TV

The Suite Life of Zack and Cody - Actual Closet variant, completes the homage by having their mother open the door so that everyone tumbles out.
Seinfeld - Elaine moves into a janitor's closet so she can order food, and Jerry and the gang drop by.
Done in Yes Minister with a really small rail carriage and an endless series of visitors, one of whom is very fat.
Star Trek: Deep Space Nine: a confirmed homage in "The Circle", though it's in Kira's quarters rather than a closet and it's pretty much friends barging in intending to wish farewell privately. All done in one take, though the final cut has reaction shots cut in.
In an episode of Flight of the Conchords, Jemaine moves into a new apartment, which is really just an empty cleaning supply closet. The first thing he does is invite over everyone he knows for a housewarming party, which naturally spills out into the hallway.