My absolute favourites would be Sugarcubes and Cardigans, both strong influence to my own music. I have all the albums from these two bands and Nina and Bjork's consecutive solo work. I like Kenickie as well.
I also listen to Otep, and some songs but not all from In The Moment. Maria Brink from ITM has good vocals but I feel the band's style limits her expressiveness. I'm not a fan of Evanescence because I had their demo album and the vocal in it was horrible. The only time I liked Amy's voice was in Korn's unplugged.
Goldfrapp is ok, they sounded better with a backing orchestra.
I like the song from Twilight but hated the movie. Was that done by Paramore? Never caught the Paramore or emo movement bug.