Although it is hard enough to find players who are willing to play normal RPGs. I can't imaging finding people who would be willing to sing out their actions too.
The musical that would make the easiest transition to RPG would be Guys and Dolls.
First off, nobody is allowed to use contractions unless they are singing.
And second, the songs are repetitive and the lines of the songs are really long, so it would give you time to come up with a rhyme if you were just singing off the top of your head.
"A lady doesn't leave her escort; it isn't fair; it isn't nice. A lady doesn't wander all over the room, and blow on some other guys dice."
The setting is familiar to people, prohibition era gangsters trying to set up temporary illegal gambling dens. Excuses to go into the sewers and abandoned buildings. Dice are even part of the setting. Maybe craps could be used to determine the frequency of random encounters. "Craps, oh no, and it is an eleven, which means that I am picked up by the police."
First pass of the list (ones I've seen) Ghostbusters West Side Story Aliens The Lion King Smokey and the Bandit (hey, it was my favourite as a kid!) Star Wars Eternal sunshine of the spotless mind Monsters Inc. rocky horror picture show Enter the dragon clockwork orange beatle juice Back to the Future Apocalypse Now Blade Runner Dr. Strangelove Dawn of the Dead Blues Brothers From Dusk till Dawn The Good, The Bad, and The Ugly (All the Dollars Trilogy Really) 2001 a Space Odyssey The Hunt for Red October Indiana Jones and the Last Crusade Alladin Falling Down Mars Attacks One Flew Over the Cuckoo Nest Groundhog Day Babe K PAX The Imaginarium of Dr. Parnasus Fargo Snatch A James Bond film (haven't seen many of the older ones, so I'm not sure which one would be the most useful) Godfather Braveheart Little Shop of Horrors Mystery Men The Sinbad trilogy (7th Voyage of Sinbad; Golden Voyage of Sinbad; Sinbad and the Eye of the Tiger) Falling Down The Shawshank Redemption The Good, The Bad, The Ugly Evil Dead Crouching Tiger, Hidden Dragon Grease Wall-E A Funny Thing Happened on the Way to the Forum Chicago: The Musical The Sound of Music Amadeus Big Trouble in Little China
Ones I've not see (and thus can't judge a game on) duck soup rocky El Mariachi (The whole "Mariachi Trilogy" actually) Ghost Dog: Way of the Samurai Bubba Ho-tep Scott Pilgrim vs The World Havery Tetsuo, the Iron Man El Topo Primer Hard Candy Mystery Train Buckaroo Banzai Pi Up The Circus of Dr. Lao The Three Faces of Eve Rent Grosse Point Blank Italian for Beginners Insomnia Seven Samurai The Prestige Astroboy Soilent Green
Next steps Right, let's take the top list - CA is there anything on there you haven't seen? We'll remove those (sorry)! Then we'll do a little bit of a cull to reduce the films by genre. For example, I like Evil Dead and Dawn of the Dead but we only really need one.
Also, should we remove some of the films whose tropes are already embedded in RPG culture: I'm thinking Bladerunner and Star Wars.