It's funny, people always say Hairspray, but I actually found it to be the reverse - the musical just can't stand up to the grimy, funky, legit doo-wop and motown of the original. I know I'm a minority opinion on that front, though.
Anyways, La Cage aux Folles comes to mind, at least the original 1978 film. The movie is fine, pleasantly frothy, but though the musical isn't necessarily a heavy-hitter, it adds a certain dimension and elevates the story. The placement and construction of the songs is so inspired, just funny enough where they need to be, and with just enough sentiment elsewhere ("Song on the Sand" is legit). Hello Dolly has been mentioned, and of course Mame is much the same - as great as Rosalind Russell is in the title role, it's impossible not to hear those fabulous songs playing in the back of your head throughout.
From what I recall, most of Pygmalion is left entirely as is in My Fair Lady, which explains why it's eight hours long, and watching/reading it now feels like seeing My Fair Lady with the songs removed. Slightly more obscure, but if you go back and read the original Kaufman/Hart Merrily We Roll Along it hews astonishingly closely to the musical.
Also, a reversal: I badly miss the choral parts of Sweeney Todd in the film.