Remakes sometimes get a bad rep because the original film was excellent, thus their existence is often seen as redundant and clearly deficient in regards to quality. However, this is not always the case. For example, Adrian Lyne's 1997 film, Lolita could be seen as sort of a remake of Kubrick's Lolita, and both are obviously based on the Nabokov novel. Clearly, Lyne's film is the better attempt because it is more faithful to the novel, and Kubrick himself was unhappy with his work, as he felt the censors prevented him from making the film into what he really wanted it to be (i.e. making Lolita seem 14-16 instead of 12, including no sexual scenes). Nabokov's relatives also strongly prefer the 1997 version, because it is far more faithful to the novel than the Kubrick film.
I also strongly prefer Tim Burton's remake Charlie and the Chocolate Factory to the original Willy Wonka and the Chocolate Factory. The original frightens me immensely.
There are also some films which should have never been made, both in original and remake form. Mel Brook's The Producers comes to mind...
Films I would never like to see remade (too lazy to put in italics):
The Last Unicorn
Der Untergang
The Empty Mirror
Quills
The Harry Potter Film Saga
Venus
But I'm A Cheerleader
Onegin
Loving Annabelle
American Beauty
Triumph des Willens (don't see this happening lol)
Edward Scissorhands (Michael ?d this film)
Amadeus