The grudge- Juon
The Ring - Ringu
Pulse- kairo
The eye- Gin Gwai
Thats all I can remember

Oh I also know that Dark Water was a remake but i dont know the name.

Oh and also if you are interested in watching anything japanese inspired, watch the Masters of Horror episode called Imprint, it's directed by a fantastic japanese director Takashi Miike.

thanks! ...I usually buy used tapes or dvd's (when I can afford to), so I'll try to keep my eyes open. Are they all subtitled?

yes

I know its not japanese, but can I recommend the brilliant Korean film 'A Tale Of Two Sisters'. Its also subtitled. Also 'Dark Water' is a film called 'Honogurai mizu no soko kara'/ 'From the Depths of Dark Water'

Per Wikipedia -

The Ring ~ Ringu
The Ring 2 ~ Ring 2
The Grudge ~ Ju-on: The Grudge
The Grudge 2 ~ Ju-on: The Grudge 2
The Grudge 3 ~ Ju-on: The Grudge 3
Dark Water ~ *same name*
Pulse ~ Kairo
One Missed Call ~ Chakushin Ari

It's important to note on the Grudge counterparts that they are the ones that have Grudge in the titles. There are two films out named Ju-on and Ju-on 2, but they are different storylines then the American versions

Other Japanese horror films that follow the plot lines in the above-mentioned films, but have not been "Americanized"

The Grudge Series:
Ju-on
Ju-on 2

The Ring Series:
Rasen
0: Birthday
Kanzenban

One Missed Call Series:
Chakushin Ari 2
Chakushin Ari Final

Thanks for all the info. ;)
I finally watched the American version of "The Grudge" several months ago, but I can't really say it did much for me. I'd love to see the original, so I could compare them.
A few days ago, I watched "The Eye 2" (by the Pang brothers), and I enjoyed that a lot more. I know it was supposed to be horror, but it definitely had me thinking more about reincarnation than the horror elements afterwards.

I really believe the Japanese versions are scarier, you just have to get past the language barrier and read the captioning.