Favorite Female vocals that give you goose bumps

Almarg - I'm a bit surprised as well, although looking back over some of the suggestions I'd say that most were not in the conventional, poorly engineered 'pop' category (though certainly some are). In the spirit of your post I'll add four I haven't seen so far; two classical, one alt-country, and one blues/soul/jazz:

Cecilia Bartoli

Anna Netrebko

Margo Timmons (Cowboy Junkies)

Casandra Wilson

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