A recent thread reminded me of Lucinda Williams. Her voice is immediately recognizable, and though her pitch is often not-quite-on (though not nearly off as, say, Johnny Cash), her singing just oozes character and personality---far more important to me than pitch perfectness.
Since I doubt anyone else has mentioned her, I have to insist: Tammy Wynette. My all-time favorite female singer, by far. I fell in love with her the instant I heard her voice. The only still-living singer within shouting distance of her is, as I have previously opined, the sublime Iris Dement, an Angel sent from Heaven.