One Flew Over the Cuckoo's Nest is a good example. Definitely better than the book IMO.
Fight Club? Interesting...but I think they are just very different. The chapter in the book about what he put in the food when he worked as a waiter...well, it's not in the film.
LOTR? OMG, sacrilege! What!
I liked the first film very much, but after that they went down hard. To compare to the book? Ludicrous! They should have made six separate movies faithfully mapped to the original six books. All that story-line flipping made me dizzy.
BTW you need to read the Silmarillion and the Lost Tales to appreciate the poetry and just who Gilgalad was and why you should care