As for best remake, I can't think of too many off hand. How about Scarface. It was a well imagined reworking of the original concept and is a good film in it's own right. Unless you're squemish of course
The Man Who Knew Too Much 1956 is better than the 1934 version
if you want to get into loose versions of....
then North By Northwest is a brilliant remake of all of Hitchcocks previous innocent man who is seen to be guilty films.
John Carpenter's 1982 remake of The Thing... the 1951 original wasn't bad, but the remake is possibly the ONLY time I've seen a film benefit from a bigger budget and more sophisticated special effects.
Little Shop of Horrors! The Rick Moranis version is millions of times better than the Jerry Lewis one. Plus its got loaRAB of groovy tunes *dances around singing Im a mean green mutha from Outer Space*