A well-known example is the first Harry Potter book and movie.
British author J.K. Rowling titled her first book Harry Potter and the Philosopher's Stone. Scholastic later published the book in the U.S., changing the title to Harry Potter and the Sorcerer's Stone. When Warner Brothers bought the movie rights, it kept the American book title in the U.S.
Rowling claimed that she regretted this change and would have fought it if she had been in a stronger position at the time.
Scholastic thought that a child wouldn't buy a book with the word 'philosopher' in the title. The U.K.-based Harry Potter Teaching Resources site suggests that the book was retitled "...presumably to make it sound more magic orientated rather than philosophy orientated." They also may have doubted American grade-schoolers would be familiar with the mythic philosopher's stone, a mineral substance that could transform base metal into gold.
As a result of the name change, all the scenes in the movie that mention the stone were filmed twice, once with actors saying "sorcerer's" and once with them saying "philosopher's." Same for the book -- "philosopher's" was replaced with "sorcerer's", along with other editing to reflect different British/American spelling differences (e.g. colour vs color). and usage (crumpets vs. muffin). The latter I find curious, since the book/movie actually takes place in England.