I thought there were a few gaps in the 30 Cult Movies That Absolutely Everybody Must See, specifically in the musicals department so I wrote my own list. Similar rules apply: flopped or disappeared on release, cult following optional.

14. Xanadu

Ranked at 14 for having the most name recognition, Xanadu is a musical with Sandy from Grease as a Greek Muse on rollerskates, Swan from The Warriors also on rollerskates and the musical stylings of ELO.
Also inspired the invention of the Razzies.

13. Rock and Rule

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Lou Reed, Iggy Pop, and Debbie Harry in a post-apocalyptic musical cartoon.

12. Cry-Baby

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I struggled over including this film since I feel like it's well known now and I personally know all the words to all the songs but it flopped on release and it's John Waters, the king of cult camp.

11. The Wiz

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An all-black cast of The Wizard of Oz, set in Harlem with great music. The film was a box office disaster (though it still pulled some Academy Award nominations somehow) but seeing Michael Jackson as the Scarecrow is a pleasure.

10. Shock Treatment

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The loosely connected Rocky Horror sequel that you never knew we wanted or needed.

9. Labryinth

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I couldn't find a better picture of David Bowie's pants. It's hard to remember that this was a commercial failure over the sound of so many Hot Topic cash registers now but back in my day... get off my bog of internal stench you damnable pre-goblins.

8. Beyond the Valley of the Dolls

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Russ Meyers directed it. Roger Ebert wrote it. The kind of film where you watch a 3 piece rock band play but hear saxophones. You probably already know three quotes from it

7. Velvet Goldmine

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This what happens when you decide to remake Citizen Kane about David Bowie and the history of glam rock and Bowie refuses to license his songs ... a gorgeous and creative feast for your glittery eyes.

6. Rhinestone

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I can't even begin to break down the plot of this movie but it's a romantic comedy musical where Dolly Parton transforms Sylvester Stallone into a country western singer in two weeks. So, "My Fair Cowpoke." There is also yodeling and references to jock itch.

5. The Phantom of the Paradise

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de Palma does Faust. And the Phantom of the Opera. And The Picture of Dorian Gray. And a little Tommy. Not to be confused with Kiss meets the Phantom of the Park.

4. The Wicker Man

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I don't think there is a specific definition of how many songs have to be performed by characters within a film's story to define that film as a musical but "Willow's Song" alone would qualify this film for me. The creepy, campy songs throughout (aside from the literal cult in the film) make the original film perfect.

3. Streets of Fire

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The first film in a planned trilogy before it bombed , this is the ultimate example of the 80's obsession with the 50's. Also "I can dream about you" is a pretty great song.

2. Ladies and Gentlemen, the Fabulous Stains

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Diane Lane was 15 in this finally released gem from '81 (it used to air on USA's Night Flight but was never officially released in theaters.) It foreshadows the advent of reality tv, was an inspiration to some third wave feminists, features members of the Sex Pistols and the Clash, and it is punk rock at its finest. I wanna be a professional!

1. The Apple

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It's the creation story set to disco. It's the distant future of 1994 where everyone wears denim and gold lamé. It's the apex of miming lyrics. At the opening night when LPs were given away as part of the show, people threw enough to damage the movie screen.
God drives a gold Cadillac. The Devil also acted in Red Dawn.

*edits for formatting. My bolds keep unboldening.