the melancholy of haruhi suzumiya
I am now 5 episodes in (looking for another source for ep6 (although haven't actually tried yet) as mine is broken for ep6), and it is weird and has some mystery in it, but not quite spooky.
I get that it is building up though, and I am not far in, and I may see more spooky stuff soon. I will definitely be keeping up with it though.
So far I think most of the content has been the moe time-traveller girl being loveually harrassed by Haruhi, for the most part lol.
Are there any other anime that are perhaps closer in theme to Ghost Stories (although obviously not with the jokey obscene dubbing lol) or even like the X-Files?
I guess I just want your regular ghost/demon defeating serial of stories.