kd lang singing Leonard Cohen's "Hallelujah". I agree with Shadorne about Joan Baez singing Diamonds and Rust and would also suggest some of her earlier work on Bob Dylan songs.
Then, to go in another direction entirely, there are those songs that give goose bumps because the singer is putting everything she has into the song. A lot of Aretha, Janis in "(Take Another Little) Piece of My Heart," and even -- guilty pleasure confession -- "Total Eclipse of the Heart" by Bonnie Tyler. (Hope that doesn't get me banned.)
Then, to go in another direction entirely, there are those songs that give goose bumps because the singer is putting everything she has into the song. A lot of Aretha, Janis in "(Take Another Little) Piece of My Heart," and even -- guilty pleasure confession -- "Total Eclipse of the Heart" by Bonnie Tyler. (Hope that doesn't get me banned.)