I disagree.
Good horror remakes (tell me if you agree):
The Thing
The Ring
Night of the Living Dead
Invasion of the Body Snatchers
Dawn of the Dead
Village of the Damned
13 Ghosts
Texas Chainsaw Massacre
The Grudge
The Fly
IMO off the list you wrote, the only really good remakes were The Fly, The Thing and Invasion of the Body Snatchers. But even those remakes are over 20 years old (going back to my "most movies these days are crap" statement.)
I watched about 3/4's of the Texas Chainsaw Massacre remake, the only reason I made it that far was because of Jessica Biel. That movie should have never been remade...same goes for the Dawn of the Dead remake. People need to come up with some new ideas and quit fucking with classics.
The Ring sucked...you really liked that crap? I liked Ringu though. The Grudge? lol I guess we just have really different taste in movies.
I can't speak for Mothman Prophecies because I haven't seen it.