The original Ladykillers is one of the funniest films ever, so even though I usually love the Coen Brothers, I was very skeptical when I heard about their remake. But it turned out to be a good and (as in the OP) quality movie, though not as good as the original nor one of the Coen’s best.
Sorcerer is a remake of a French movie, The Wages of Fear. Haven’t seen all of TWoF, but Sorcerer is awesome and full of tension.
The cartoon version of The Return of the King wasn’t nearly as good as the later Peter Jackson movie … although I admit, the song “Where there’s a whip, there’s a way” is very catchy. 
The Spencer Tracy/Elizabeth Taylor Father of the Bride was a classic I adored, and when I heard it was being remade, with Steve Martin in the Tracy role I was sure it would be awful.
I couldn’t have been more wrong. The remake was just as lovely and sweet as the original.