First @Kindablue, I was pleased to see that your Poe link was highlighted for me as a link I'd already visited. She has a few songs that don't work for me, but she also has a bunch that are among my all-time favorites.
Sarah Blasko (this video is one of the most beautifully filmed I've ever seen)
Bat for Lashes (Natasha Khan)
Jem (this fan video is pretty much the only reason to ever have anything to do with the movie Ultraviolet )
St. Vincent (having worked in a bookstore that hosted music events, I can say this video is frighteningly accurate)