I wholeheartedly agree that Ring is outstanding (if only the same could be said for Gore Verbinski's godawful remake) though the sequels didn't really live up to their predecessor. Ring 2 was promising but the ending was extremely weak and Ring Ø: Bâsudei took a turn for the Dawson's-meets-Carrie - and didn't do either of them particularly well.
Rasen, or Spiral, is the 'sequel' they made alongside the original then completely disregarded à la Halloween 3. It follows Koji Suzuki's books (which incidentally they sell in Ottakar's) more closely than Nakata's but it's hard to find Sadako quite as frightening when she crawls from the TV, grinning and naked, in the form of Japanese ex-model Saeki Hinako...
And speaking of Hinako, Uzumaki is movie that's light on the plot but very pretty to look at.
Miike Takashi's Audition has a wonderfully twisted ending though Dead or Alive (which, I'm aware isn't a horror but still) is as hilariously bad as it is inconsistent.
Natural City, a Korean take on Blade Runner except that I actually enjoyed it, is again not a horror but definitely worth watching nonetheless.
Battle Royale is great. Battle Royale 2 is distinctly less so.
Tetsuo is appallingly bad.
As for remakes, well, I've already explained my position on The Ring though I'm still slightly intrigued to see The Grudge (remake of Ju-On). Much as I love Buffy, however, I'm not so sure Sarah Michelle Gellar would've been my first choice when it came to casting the lead. Also, the posters and trailers seem more than a little familiar:
http://advision.webevents.yahoo.com/sony/thegrudge/
Now where have I seen that face before...?
The only horror I felt watching The Happiness of the Katakuris was realising I was never getting those 2 hours of my life back, Silent Hill is indeed amazing and The Eye is in fact Chinese.