Translating a book to film is somewhat analogous to translating literature, particularly poetry, from one language to another. If the translation is too literal it risks failing in the target medium, whereas if it’s too idiomatic then it risks reshaping the source material.

In the case of LOTR, as you say, the changes made for a better film, while remaining true to the source material, and so were entirely justified. The Hobbit, on the other hand, was a complete travesty, partly because they practically rewrote the story.

“Translation is that which transforms everything so that nothing changes.”

– Günter Grass

The film was a near perfect rendition of the book. The only other case I can think of like that is LOTR.

So many things about that film are spot on - the casting, the direction, the music (Pixies, Dust Brothers). Again, LOTR also hit all the right notes in that respect.