Honestly, I think movies should only be remade if there really is room for improvement with the original. There should be an actual point to remaking it (i.e. a better reason then, "we have better CGI" or "newer is better"). If a movie is considered a classic, there's no point in remaking it because you have nowhere to go. Remakes work the best when the original movie is not particularly well known, (ex."Angels in the Outfield") or when the original concept is used but the actual story is taken in a completely different direction (ex. the original "Ocean's II" and its remake share a similar concept but, have radically different plots).
Remakes of foreign movies that have been adapted for American audiences I barely consider to be remakes since they have, actually, had to adapt the story for a different culture, making it more of an adaptation of a story than a straight-up "remake" (the best example is "The Magnificent Seven" based on the Japanese classic, "Seven Samurai"). That somewhat goes for musical remakes, as well, because the actual genre of the movie changes, taking the movie in a different direction right from the get-go (ex: "High Society" & "The Philadelphia Story"; both considered classics when one is simply the musical adaptation of the other). It can, also, make a difference if a movie is based on something of greater importance than the film itself, for example, there have been many movie versions of "Little Women" but, they are rarely considered to be remakes of each other since the source material carries more weight/importance than the previous films do.
But, in actuality, the very best remakes are remakes in the truest sense of the word: when a director, literally, decides to remake one of their previous films. Obviously, a director only does this when they feel they can do better now that they have more experience and they are, virtually, always right (see Cecil B. DeMille's 2 versions of "The Ten Commandments", Alfred Hitchcock's 2 versions of "The Man Who Knew Too Much" and Leo McCarey's original "Love Affair" vs. his remake "An Affair to Remember".)
Basically, it all comes down to what I said before: there has to be a real reason for remaking the movie other than the studio wanting to make money or a filmmaker really wishing that they had made the original. Creatively, someone has to be able to bring something new to the movie to make it worth seeing/making even when the original movie is already out there.