There are a couple of songs that spring to mind here for me:
- Prelude 12/21 - AFI (this is mostly because I associate it with a particularly creepy scene in Smallville, but the beginning in particular is quite haunting, at least in my opinion)
- March of Mephisto - Kamelot (I don't know why, but this creeps me out. It's the lyrics, more than the composition, that make this one haunting)
- The Siren - Nightwish (I wouldn't classify many Nightwish songs as "haunting" per say, but this one definitely fits the bill for the way Tarja sings it)
- Morgenstern - Rammstein (This one is haunting, to me at least, because it is so unbelievably atypical of Rammstein, and the lyrics are more baleful than they are outright aggressive)
- Angels - Within Temptation (although a lot of pre-Heart of Everything Within Temptation songs could be said to fit this description, before Sharon changed her vocal style to something noticeably more aggressive. Not that it's a bad change, but it's just that: a change)
I could name plenty of tracks from anime and video games. Karasu's second theme from Noein, for example, is probably the most haunting piece I know of from anime, and Psycho Mantis' theme from Metal Gear Solid is definitely high up on the list for video games) but not many actual songs spring to mind, so its a rather sparse list from me...unless you want me to include tracks from games, anime and films, in which case that list will probably multiple itself by ten at the least.