There are so many songs I consider "haunting" that I love... Here are a few lesser-known ones, and I will likely share some more of my favorites as soon as I can think of them... ;p
"Let It Go" - Grace Slick - this track takes time to grow on you - but it really is an awesome song (around the 3:00 mark, things get REALLY interesting!!)
"Garden Of Man" - Grace Slick - the last track from her 1980 solo album Dreams - an excellent album!
Sissel Kyrkjebø is a Norwegian singer who probably has the most beautiful soprano voice I have ever heard. If you have ever seen James Cameron's Titanic, you have heard her voice as she is the one doing the vocalizations throughout the soundtrack. Most of her music falls into the categories of pop/classical/easy listening/folk:
"Dusk" - Sissel - 1st song I thought of when I read the initial post - lovely, beautiful, haunting - gives me goosebumps
"She Walks In Beauty" - Sissel - probably even more haunting than the last, but also very lovely - this one is from the Vanity Fair soundtrack
Porcupine Tree is a modern prog-rock band formed by Steven Wilson:
"Lips of Ashes" - Porcupine Tree - nice layered harmonies, and like most of their stuff, very nice production
"Buying New Soul" - Porcupine Tree - very haunting keyboard riff starts this piece out, and it's really an interesting song
"Russia On Ice" - Porcupine Tree - some haunting sections, some beautiful sections, some not-so-beautiful sections - overall an interesting piece of prog-rock
Hope some of you will enjoy them!