In terms of ones that can give me the chills, some more modern ones that some immediately to mind are:
1. Fiona Apple. The girl could seriously sing me to you know what. Anything off of Tidal to me is beautiful.
2. Sarah McLachlan
4. Alanis Morrisette. Incredible pipes.
5. Mazzy Star (mentioned above.) Hope Sandoval is a serious artistic waif fantasy of mine.
6. Sia. Seriously underrated I think. Breathe Me is a particularly nice one, and the song she did with Zero Seven, Waiting Line, is gorgeous as well.
7. Natalie Imbruglia is gorgeous and did some great songs n the 90s.
8. Mia Doi Todd, which probably none of you will have heard of. She did a couple of really beautiful records as well back a while. Probably has continued but I'm not as up on them as those first ones.http://www.youtube.com/watch?v=Wt-t67DtVO4http://www.youtube.com/watch?v=HEVLxsZMx10
9. Natalie Merchant
10. Regina Spektor
11. Vienna Teng. Her album "Dreaming Through the Noise" is gorgeous. This song is paritcularly nice (it has nothing to do with the video it's been put over here.) Listen to this one in full resolution on a nice system.http://www.youtube.com/watch?v=14P72nLQmRI
12. Tori Amos. Her "Little Earthquakes" albums is still great to go back to.
13. Lisa Germano. She started out as John Mellencamp's fiddler then went out on her own. She does very personal and experimental stuff, but some of it is gorgeous.http://www.youtube.com/watch?v=aoLMqGCHrwM
14. CocoRosie. I have been trying to get people hip to them for a while. There are two female vocalists in this case. They started off very primitive but some of their stuff is just amazing.http://www.youtube.com/watch?v=51K4cUTuvc0http://www.youtube.com/watch?v=zDb7dAnm79Ihttp://www.youtube.com/watch?v=c6bInhOhUYs