The American Theatre Wing published an interesting article called "37 Flicks Theatre Lovers Should Know." It is a great mix of new and old, popular and obscure. What is fascinating about writer Howard Sherman's approach is how he defines "know." He is not suggesting you need to go out and watch all 37 of these features; he warns against watching camp classic Stayin' Alive, but includes it because the entire focus of the film is the stage. He thinks that having knowledge of these films is important to an understanding of the stage as presented on the screen. You don't need to see the metallic-leotards of Stayin' Alive's finale to know that Tony Manero was not cut out to trot the boards on the Great White Way.
There really is something for everyone (save the rock theater fan). There are classic musicals, like Summer Stock and 42nd Street, as well as post-modern/ironic musicals like Hamlet 2 and Camp. There are farces like Bullets Over Broadway and Waiting for Guffman and melodramas like All About Eve and Stage Beauty. You already knew about those films, though, didn't you?
What about his recommendation of Weeds? It's a 1987 film in the history of the great "put on a show" pictures, only it takes place in a prison. I hadn't heard of it before, but now that I've read his description, I've seen it parodied many times in popular culture.
I didn't even know that there was a theater slasher outside of the backstage drama/the production is in peril pictures. Now I'm trying to track down a copy of the Lauren Bacall starring The Fan, about a starlet being stalked by a crazed devotee. Sure, he deliberately says "this is one you can miss," but I am nothing if not a fan of bad horror movies.
Perhaps the most interesting discovery for me on the list is The Band Wagon. He compares it to Singin' in the Rain only for Broadway musicals. They have the same screenwriters, too. The difference is how Band Wagon starts to riff on Faust in the producer's quest to make the show a success.
Howard Sherman produced this list with suggestions from his Twitter followers, so even he hasn't seen all of the films. It was an interesting experiment that has yielded a pretty hefty comment section for a theater blog and an interview with the New York Times regarding the creation of the list.
I'm going to add a few suggestions on top of his intriguing 37. The devastating Dancer in the Dark would be nothing with the community theater production of The Sound of Music that tragic heroine Selma plays the lead in. It adds levity, then sadness, to a very dark film.
As far as I'm concerned, one of the best sequences in Annie is when Daddy Warbucks brings the titular orphan to see Radio City Music Hall. They get to watch The Rockettes' Floor Show before their feature film plays. It's a beautiful sequence placed at just the right moment.
Rocky Horror Picture Show features a lot of floor shows, doesn't it? There's "Time Warp" and the "Floor Show" sequence, too. Since Dr. Frank-n-Furter is always trying to gain attention, you can argue "Sweet Transvestite" and "Charles Atlas Song/Reprise" are floor shows, too.
The action of Rosemary's Baby all stems from Guy Woodhouse's acting career and what he's willing to do to succeed.
While both versions of The Producers made the list, I would point out that at least four of Mel Brooks' other features use stage genres to advance the story and include a flashy musical number. There's Bernadette Peters as the irresistible ingenue of the aptly titled Silent Movie. Then there's Madeline Kahn as German canteen chanteuse of Blazing Saddles, complete with military-garbed back-up dancers during the floor show. It's hard to forget the incredible "Puttin' on the Ritz" sequence of Young Frankenstein, even if you want to. And then there's High Anxiety, which features Mel Brooks himself singing the theme song in an impromptu lounge show.
Is there a version of King Kong that isn't driven by wanting to exhibit the massive ape in the heart of Times Square?
There are many more films about the craft and culture of theater. Howard Sherman's list is simply a great starting point.