First of all, hi! (this is my 1st post here!)
I love both versions of Ring, the original because it's a fantastic introduction to eastern cinema (by the way, check out 'Dark Water' and 'The Eye', if you liked Ring, you'll like these), and the remake deserves credit for the fact (in my opinion!) that it is equal to the original in quality, and respecting of it. How many remakes have we seen that are utter pants!
I have to agree with an earlier post about 'the forgotten sequel' Rasen (Spiral), it isn't very good, but worth a look if you're curious. If they were to go on to make the film of the third book (Loop) I may hunt that one down too!
If you havn't done so already, check out Ring 0, while it keeps you on the edge of your seat it's also utterly heartbreaking. You'll actually feel sorry for Sadako!