OK, here are a couple of remakes where the remake is better in many ways than the original, but the original still has good qualities that the remakes have lost. I like to watch both the original and the remake because I get different things from them.
The Man Who Knew Too Much
and
The Ring (Ringu)
Not a remake but a spoof - and a very funny movie.
Check out “The Man Who Knew Too Little” with Bill Murray.