Broadway Legend Joined: 12/5/04
If Jesus Christ Superstar qualifies (and I think it does), then Dracula the Musical should, as Dracula = Vlad the Impaler. Jackie: An American Life, about Jacquiline Kennedy Onassis. Not a musical, but Jack: A Night with Barrymore
The Sweet Smell of Success.
Sweet Smell of Success is based on the film of the same name. While, yes, the main character of the film (and novella) is inspired by a real person (Winchell), the plot is not based on real events.
Also: LoveMusik
I guess I was going by the "inspired by" part of the op's question (as were several of the other answers before mine).
Broadway Star Joined: 2/13/06
It hasn't techically been on broadway, but "Martin Guerre" is based on a true story.
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