I immensely enjoyed "Hello Dolly," "Gypsy," "South Pacific," the aforementioned "The Pajama Game," on stage among others but only a small handful made it successfully to the screen. Some made it to television through PBS as a video of a stage production. "Sunday in the Park with George" is one of those that's great on video, the revival of "Kiss Me Kate" is a hoot -- "Brush Up Your Shakespeare," yet the earlier filmed version is rather clunky until the dance number come on. The original black and white "Show Boat" directed by James Whale who also gave us "The Bridge of Frankenstein" is a beautiful film, the remake with Howard Keel, Katherine Grayson, and Ava Gardner is colorful, vibrant but curiously flat (and the songs are sung extremely well, Ava being dubbed, of course).
I love the PBS "Sweeney Todd" with the original broadway cast, but as its own cinematic horror movie with music, the filmed version with Johnny Depp is very effective.
I mentioned some poor adaptations and can add "South Pacific" which was overlong and those awful color filters were jarring and unnecessary. It was episodic and kept faltering like it had a flat tire.