The most successful adaptation of a book that also stayed remarkably close to the source material: the first Harry Potter movie. I read the book just before seeing the movie and I was constantly surprised how closely they kept to the original story, while still taking advantage of the different medium. The other Harry Potter movies have suffered from the fact that the later books are much longer than the first one, so whole swathes of material have to cut out.
I agree that the LotR movies are mostly faithful adaptations, but I still don't get why they changed some things, other than a suspicion that Peter Jackson, et al, actually believe they can write Tolkien better than Tolkien.
A bad adaptation that I felt was better as a movie is The Postman. Granted, I don't have a knee-jerk hatred of all things Costner, so that helped. But mostly I found David Brin's book to be incoherent, with a horrible ending.
Another bad adaptation that was a fun movie is I, Robot. Though I'd still like to see the original stories turned into a movie or short series, as the stories are good, classic Asimov. (Or better yet, the Foundation series.)
Amazingly, The Omega Man (bad as it is) is a much better adaptation of the original story than Will Smith's I, Legend. But Smith's is the better movie, IMHO.