Three examples of films I enjoyed in their original form, and then despised in their Hollywood versions.

Der Himmel uber Berlin: Probably one of the most beautiful films I have ever seen
City of Angels: I really have no response, except maybe why?

Spoorloos: A fantastic psychological thriller.
The Vanishing: The Hollywood version actually changes the ending. This is an abomination.

La Femme Nikita: Quoted from imdb, "This, the French La Femme Nikita, directed by Luc Besson, is one of the strangest, most bizarre, yet psychologically truest movies ever made".
Point of No Return: Again from imdb, "The French would be embarrassed if they saw this remake. Rent the original, trash this one."