The Lord of the Rings

Don't get me wrong, I love those books to death and have destroyed more than one mass-market paperback from over-reading. It's importance and contributions to the fantasy-genre can not be overstated. They are nothing short of a treasure.
But, Tolkien needed an editor. Everything to do with the Hobbits after Fellowship were an absolute drag to read through; it took me thrice as long to read the Hobbit bits of Towers than it did to read the rest of it. So much text was spent of inconsequential details and worldbuilding (though as a worldbuilder, I understand).

Peter Jackson's films trimmed a lot of the fat. Sometimes too much, but overall I think the narrative was better for it. As a bit of a book-purist I was initially upset at the omission of The Scouring of the Shire in The Return of the King (2003) . However, it is quite an odd chapter. It's a very good example of the end of the Hero's Journey — Our Hero crosses the return threshold from the Special World, having changed. There, and back again. But the manner in which it was written is... strange. Tolkien said that he drew on his childhood during the end of the 19^th century, and it clearly came from a very personal place. Narratively however, it doesn't quite fit. Overall I think the films improved upon the source material, even if the omission of Tom Bombadil was a veritable crime.

I found The Expanse TV series better than the books.

In part, the first novel suffered from typical "first novel" writing problems - lack of clarity in some scenes due to background, dialogue or plot fuzziness; too many characters introduced; continuity issues; insufficient or excessive explication...

This gets cleaned up by the authors as a result of more mature writing skills by the time they're writing for the series production. I've also gotten the sense from a couple of interviews that they really wanted to be writing for a visual medium in the first place.

Between the careful scenery building and cinematography, the series clarifies a number of things that were unclear. The books made a good effort to describe and add excitement to space travel, but the visuals of the grim, claustrophobic, clanking, fragile tin cans of the future and the horrors of war or contagion in those miniscule habitats, are very fully realized.

The text version of Holden's character was also a deeply annoying "Mary Sue", a heroic projection of the authors' fantasy-selves, with other characters barely sketched in around him as backdrop for his exploits. The series does a far better job of realizing other characters and setting Holden in place among other actors who have personal motivations and agency. The distinctions of Belter and Martian culture from Earth are better realized as well.

Im going to be that guy and put the obligatory Game of Thrones in here.
And yes, it is because he has written himself into a corner and taken elventeen million years to put Winds of Winter.
I read all the books so far before the show started and am overall pleased with the show and the characters.
The books had chapters I would skip (sansa whining, catelyn being a cunt, and dany doing nothing) where as the tv show skipped most of that due to its format or just being dropped entirely (yay, no stoneheart bullshit!).

'The Martian' movie was better than the novel.

The novel read like a series of engineering test questions, and was extremely dry reading. I loved the premise and enjoyed the plot, but I found the technical detail a bit overwhelming. And the protagonist, Mark Watney, was a bit full of himself!

The movie was much better. It removed the dry engineering texts, and replaced them with action. Also, Matt Damon's version of Watney was more relatable than the novel's version.

There was one big flaw in the movie: it removed the suspense by showing us the rescue efforts too early in the narrative. In the novel, Mark Watney believed he wasn't going to be rescued and so did we readers. This raised the stakes for his efforts to keep himself alive. In the movie, we saw the rescue attempt being developed. Also, in a book, there's always the slight possibility that the protagonist can die, but that was never going to happen in the movie!

Fight Club is a much better movie than book. The book's ending is strange and a bit left field deus ex machina compared to the movie's.

Similarly, the Mist may work better as a movie than a book due to just a change in the ending—a change so good, Stephen King himself was blown away.

While I don't know if I would say the book is inferior, I saw 'Annihilation' recently and I thought it was a perfect example of an adaption that captured the spirit of the work while being substantially different. Many film adaptations struggle with toeing the line when it comes to being faithful to a book vs. being an adaptation. Lots of fans of the book will be upset over artistic changes while lots of producers recognize that not everything that works in a book can translate into such a visual medium. I watched the adaptation of 'The Great Gatsby' starring Robert Redford recently and that film works so hard not to stray from the novel with rather mixed results. 'Annihilation' feels more like a half-remembered adaptation of the novel that was fleshed out to make it work. As if you read it a year ago and out of the blue were asked to write a script based on what you did remember. I think all of the important conceptual points were still hit while allowing it to use the strengths of film as a medium.

I'm probably really dating myself here, but I think Jaws is probably one of the best examples of this, especially as the movie is a classic that helped to define the summer blockbuster, while the book is probably not widely known these days. I'd say the main reason the movie surpasses the book, even setting aside the visual spectacle, is that the film spends a lot more time with the characters (particularly Brodie), makes Quint more interesting and human (adding the element of being a survivor of U.S.S. Indianapolis, removing the baby dolphin as bait element), and eliminates a number of the less interesting subplots (the Mafia angle, the Hooper/Ellen Brodie affair).

I find the play/movie adaptation of 'Auntie Mame' to be better than the book.

The book is a collection of amusing anecdotes about the fictional Patrick Dennis's equally fictional Auntie Mame, but it can be a bit dry at times. It's also somewhat dated, being published in the early 1950s.

However, the play and the subsequent movie, both starring Rosalind Russell in the title role, are lively. Mame Dennis becomes a real and interesting person, rather than the two-dimensional near-caricature she is in the novel. She's alive. You really do get the sense of her as a whirlwind, dragging young Patrick and sundry others along on her quest to feast at the banquet of life.

To fit the novel into a play, some of the drier or more dated episodes from the novel were dropped. Even though the play is set in the same periods as the novel, and was produced only a few years later, it doesn't feel as dated. Mame Dennis feels a bit more timeless.

The Bridge to Terabithia for me. Though the book is amazing, something about seen it onscreen just really popped for me. I remember being sad reading the book, but was devastated when I watched the movie.

How To Train Your Dragon, for sure, at least for me. In the books, the dragon which the main character Hiccup befriends, is a small wyrm-like creature small enough to sit on his shoulders.

In the movie adaptation, they turned Toothless into a big, universally-feared yet loveable, cat-like stealth fighter.