Ringu  ==>> The Ring 
Kairo  ==>>Pulse 
Dark Water  ==>> Same name 
Ju-on: The Grudge  ==>>The Grudge  This one is interesting in that the director for the original, Takashi Miike, also directed the remake.
One Missed Call  ==>> Same name 
As you can see, the 2000s saw a prodigious number of hit Asian horror films ported over,
That was quite a bit of reading so I'll split this post into two parts for you tl;dr types. How accommodating and understanding I am! (and humble!) ╮(￣ヮ￣)╭