I got the Thing on dvd a while ago, great movie (and the dvd has a nice and really long documentary on the making of as well).
The Descent was one of the best of the more recent horror movies I've seen.
Then I watched Silent Hill recently which was pretty good (obviously not up to par with something like The Thing, but for a videogame movie it wasn't bad at all, although not really all that scary).
I haven't seen all those japanese films yet... I think I saw the Ring but none of the others mentioned (I'll get around to it sometime
)
Then of course there's the scifi stuff like Alien (the first one I think could be classified as horror, and maybe Alien 3 as well, the other's are more action/thriller stuff)