I think that "Hine e Hine" and "Pokarekare Ana" when sung by Hayley Westenra are beautiful, and the opening "Scene Of The Swans" from Tchaikovsky's Swan Lake.

From more modern songs, "Hello" and "My Immortal" by Evanescence, from their "Fallen" album are very haunting, and Amy Lee's voice adds to the effect.

Haunting show tunes, as far as I'm concerned, include "On My Own", "Bring Him Home" and "I Dreamed A Dream" from Les Miserables (I've only just learnt how to stop myself crying when I hear them), "Where Is Love" and "As Long As He Needs Me" from Oliver!, "Superheroes" from Rocky Horror, "Lament" from Evita, "Memory" from Cats, and "Last Night Of The World", "Movie In My Mind" and "Bui Doi" from Miss Saigon.