I don't know if it's the best, but I found the 1997 film adaptation of Mrs. Dalloway surprisingly decent. Given that the book, aside from one somewhat gruesome scene near the end, is carried mostly by the character's internal thoughts rather than the plot itself (an upper-class Englishwoman preparing for a party and an unrelated man deep in the throes of shell shock attempting to go about the day with his wife), I have no idea how they pulled it off, but they did. That said, I'm not sure if most people would like it having only seen the film. Knowing the book allows one to play fill-in-the-blank in regards to the characters' internal thoughts, which is definitely a help.
Lord of the Rings is beyond epic, and absolutely up there amongst the cinematic greats, but they left out Tom Bombadil. And for that reason alone, it cannot be said to trump the books. Also, the Hobbit films tainted everything. I can't think of an example where the film stood up on par with the book it was based on. You just can't get all of the detail into a film, right? One that cut the right amount in the right ways was Jaws. I'd name Jurassic Park too, if they'd kept the ending more similar. I reckon Trainspotting was captured well too.
"I'll see you later". They made a perfect movie based on the book. They chose the characters very well. I advise you to watch it. The book and the movie are both good in their own way. But I warn you, you will cry.
I watched the movie first and then read the book, but I think The Martian by Andy Weir is excellent. The music in the movie is really peaceful and deep. 10/10 bought the DVD so I can watch it again.