There are some examples of remakes that are great. Frequently, these become the "classics" and people forget about the original. A canonical example is John Carpenter's "The Thing" in 1982, which was a remake of a somewhat crappy 50s movie and is now a sci-fi horror classic. Another good example is "Invasion of the Body Snatchers" from 1978, starring Donald Sutherland. It was a remake of a 1950s movie too, though in that case the 50s movie was actually pretty good, but the 1978 one was scarier.

I can't think of any good remakes from after the year 2000.