I'm sure many would disagree, but I find these remakes superior to the originals:
Invasion of the Body Snatchers (1978)
The Thomas Crown Affair
War of the Worlds
Dawn of the Dead
Well, you're right about one thing: many would disagree. The only one on that list that I'll give you as a superior remake is THE FLY.
John Carpenter's THE THING is as good as the original, but for different reasons. They're both standout sci-fi films.
The Coen Bros.' TRUE GRIT has its pleasures, but so does the John Wayne original. Two variations on the same source material, both valid.
As for INVASION OF THE BODY SNATCHERS and WAR OF THE WORLDS, I strongly disagree.
The others? I actually haven't seen the remakes.