It's a topic we speak of often, and everybody seems to love it, but nobody to my knowledge has ever made a definitive list of "songs inspired by Shakespeare" because, quite frankly, how do you define that? Do you need lyrics from the text? Character names? Plots?
365 Days of Shakespeare doesn't attempt to answer these questions, she just offers her top 10. I link because there's a couple in there I'd not heard of!
No Rufus Wainwright in the mix, by the way, but that may go back to "how are you defining this". Putting an entire sonnet to music isn't really the same thing as rewriting a Romeo and Juliet story. I have both the Dire Straits and Indigo Girls' versions of Romeo and Juliet in my playlist, and she's right, the Indigo Girls version is much better.