The most haunting music you ever heard?

"Snowed In At Wheeler Street" from Kate Bush's latest album is a current release that has that quality.
Furtwangler's recording of Tchaikovsky's "Pathetique" symphony on DG.
"Gentle On My Mind" as recorded by John Hartford in "Natural To Be Gone" also comes to mind.

michael mantler/edward gorey "the hapless child"

Rx8man it sounds like a film score. Probably science fiction or supernatural. I realize that's a fairly large genre but I don't think it is classical or even jazz so that's what I am left with.

#1 at the blue whale from the original dark shadows series soundtrack.

Rx8man,
There is a music site that has some sample clips that sound virtually identical to your link. The site is royaltyfreemusic.com and a couple of cuts that sound just like the music in that video are titled "waterlands" and "watery grave". You can use the search box in the upper right of the home page for those titles and click on the green speaker icon to listen to the clips. Unfortunately, you buy the rights to use the music from that site, and it is not so useful for someone looking just to buy a song. The cost seems to be $59.95 per track, but hey, you own it. Kind of a fun site to check out though.