As Abnegation said, John Williams has composed a lot of very famous film scores, including scores for nearly all of Steven Spielberg's films (and I don't know anyone who hasn't seen any of his films), I'm sure most people can enjoy his music. I particularly like his score for
Schindler's List, it's a wonderful (albeit saddening) film and the score plays no small part in setting the mood and making the film as great as it is.
I also enjoy Hans Zimmer's film scores,
The Lion King, Pirates of the Caribbean and
Gladiator are just a few of the famous films he's composed the score for. My favourite scores by Hans Zimmer are for
The Ring and
The Dark Knight.
I happen to notice that
Disney tend to write brilliantly when it comes to composing a score also.
I'm not sure what you mean by this. True, Disney films usually have enjoyable scores, but they still get professional composers for their film scores. As I said before, Hans Zimmer composed for
The Lion King and James Newton Howard composed the score for my favourite Disney film,
Treasure Planet. The actual Disney company aren't composers.