Most unusual/mesmerizing female voice.

Take a listen to Concha Buika, the queen of flamenco fusion. Check out "La noche más larga" and "El Último Trago" with  the great Chucho Valdes on piano. I also consider Cecile Mclorin Salvant on her debut album up there with the greats.

Elizabeth Anka Vajagic / Stillness of this day is an incredible LP

Kelly Flint from "Dave's True Story" fits the "mesmerizing" category which most posters seem to emphasize over "unusual".  When combining unusual with mesmerizing, I can't believe that in 6 years and 114 posts that no has mentioned Patricia Barber!  LUDITES! (LOL)

For me its Sarah Vaughn. She's unusual and mesmerizing all at the same time. Many excellent tenor saxophone players wish they could play with the emotional impact that "Sassy" did.  

Patricia Barber??? Really? Here albums are DRENCHED in artificial reverb. I have heard that with the 180 gram version, they finally got the thing to sound decent.