I've only seen the original Ringu and the sequel. The original is far superior, as they often are, but the follow up is worthwhile. Pretty solid twosome. No idea about any of the ones that came after.

Everyone I know of seems to regard the original being far superior to the remake.

I thought the remake was much better. Better camera work/shots/cinematography, better locations, better acting, etc etc.

I saw the American remake and didn't feel strongly about it either way. Once I've seen the original, it always seems to take the edge of the remakes for me. Particularly remakes that come out fairly close to the original.

That's one thing every remake and even sequel always has against it, they never have the freshness of the original no matter how good they turn out. The original is the original that sets everything up and thus feels the most innovative.

The Thing?

The Thing would be a rare exception given how different The Thing in both versions is.

Some may argue it's not really Horror, but The Crow is another I remembered. I've seen only the original which is excellent. I think it counts as Horror, definitely.

With anthologies I remembered the two Trilogy Of Terror films. Never saw the first but I saw the second years ago on either the USA network or Sci-Fi channel. It was pretty good from my memory and all three of the stories were entertaining. I'd like to see it again.

That's a good list, I have seen almost all of the film