The Twilight Zone, (1985-89), and
The Outer Limits, (1995-2002), were both excellent remakes, but maybe anthology shows shouldn't count.
Battlestar Galactica 2003-09 was good, and I liked the 2009-10 version of
V, but it's easier to update/ re-imagine science fiction shows.
Space Ghost - Coast to Coast and
Harvey Birdman, Attorney at Law were good, but cartoons are different from a drama or a sitcom. I'll rule out game shows as well; the current version of
Jeopardy! is better than the 1960's show. The new
The Gong Show which aired a few years ago was terrible.
List of American Sequel TV Series
The 2017 incarnation of
Twin Peaks had its moments. I can't say that any of the others on that list is any good, not including anthologies, sci-fi, and cartoons.