Favorite Female vocals that give you goose bumps

Jax2
I think I mentioned Cecilia Bartoli.

Anyone who really means what she sings.

A few come to mind...

Emmylou Harris - Boulder to Birmingham...arguably the best love song ever written because it is real.
Tori Amos - Little Earthquakes...she is crazy, though.
Sinead O'Connor - the traditional Irish stuff...she is an overlooked talent who is truly Irish to the core.
Poe - the female F. Scott Fitzgerald of our times...she is intense and utterly brilliant.
Aimee Mann - Lost in Space...You hear; you know.

Sorry, missed that Gawdbless. Tori Amos is a favorite of mine too, Mosin - there's a cut off her, "Strange Little Girls" titled, "97 Bonnie and Clyde" that's kind of hot-miked, and largely whispered...definitely goosebump rendering and really creepy...but I love it!

Jax2,
Cecilia does have a voice that would bring a tear to a glass eye.
A few less well known to the masses,

Emilie Autumn
Gitane Demone
Diamanda Gallas
Danielle Dax
Tina Root (Switchblade Symphony)
Monica Richards (Faith & the Muse)
Kim Richey
Lisa Loeb

Regarding classical performers. It seems like those recordings are not recorded the same way, with as much care, with a good mic. I don't listen to much classical for that reason.