I can think of:
Gigi - adapted from the romance novella by Colette
Jane Eyre: The Musical (Original 2000 Broadway Cast) - adapted from the gothic romance by Charlotte Bronte
And I know that The Strangely Beautiful Tale of Miss Percy Parker is being adapted as a musical
and a musical adaptation of Jane Austen's Emma is supposed to open on Broadway in 2013
Can anybody think of any other romance novels that have been adapted into musicals?