Easy call for me with The Ring, I like it as much as the original Japanese film, and I rate both highly. Both have aspects they do better than the other and have other aspects that are done differently but just as well as their counterpart (score, cinematography).
The Hills Have Eyes remake is quite good, as good or better than the Craven original.
The Dawn of the Dead remake is also quite good, though much different in tone than the original and not as much of a classic (though I can see why others may rate it higher than the original).
Thirteen Ghosts isn't among my favorites here but I respect it for being something different than the original and also as good or better than it.
My Bloody Valentine 3D is also pretty solid for a remake with a good twist. I don't like it as much as the original, but I respect it.
None of the others really approach the originals. The Grudge is fine largely due to it being directed by the director of the original so it's not bad or offensive, but it's not close to as good as the original (though it's easier to follow).