The Saruman story was completely changed, including no scouring of the shire, which really showed the Hobbits' full character arc in the books.

And the changing of the Faramir story was dumb. He was the counterbalance to Boromir in the books.

Making Arwen such a huge part of the movies was also a big departure, though that one made more sense for cinema.

I could go on, but yeah, I'm a nerd, so there's that.