The history of this screenplay is rather more complex than this. The screenwriter had a blog and gave his thoughts. As I understand it, his screenplaty started out as an original story with original characters, but set in a world of robots that operated under Asimov’s Laws. The studio got the idea to buy the rights to Asimov’s novel, change the names of the characters to those of Asimov’s novel, and market it as an adaptation of “I, Robot”, something it definitely didn’t start out as. But you can’t change a random Robot story, even one set in Asimov’s universe, into “I, Robit” by changing the female lead’s name to “Susan Calvin”. But that, apparently, is what they tried to do.
Ira Levin later said that Polanski called him during filming to ask about a particular men’s dress shirt ad in The New Yorker that had been referred to in the book. Levin admitted that he’d made it up - he just assumed that every issue of The New Yorker would have a shirt ad like that.
Of course, the film has little in common with the original unabridged Morgenstern version of the book. 
Fight Club was a faithful adaptation. Much of the dialogue came straight from the book. They changed the ending a bit…
The Pope of Greenwich Village. Unsurprising, since Vincent Patrick wrote both the novel and screenplay. He used the film medium to beef up some scenes to the story’s general improvement (like the scene where Paulie just found out Diane robbed him and left a note trying to justify her theft).
The Story of O was surprisingly reverent, all things considered. This was the golden age of X-rated art films.
As mentioned in this thread, Kenneth Branaugh’s adaptation of Frankenstein is extremely faithful to Mary Shelley’s novel. It is convincingly set in the early 19th century, and as in the novel is framed with Captain Walton’s encounter with Victor Frankenstein in the Arctic Ocean. Robert De Niro is marvelous as the creature. Even though the creature is misshapen and murderous, he is also intelligent and articulate instead of grunting and speaking in monosyllables like the Hulk. It is one of the best retellings of the novel ever made.
I thought The Fountainhead was pretty faithful, reasonable since novel and screenplay were both written by Ayn Rand, but she made some amusingly conformist changes to her story about uncompromising artistic vision.
I haven’t yet seen an edition that did more than a workmanlike lob at translating from the original Florinese. They just don’t capture the pseudo-pompous tone that Morgenstern managed simply with his choice of the absolutely proper tense for his verbs. So many folks miss that he was not just deflating Florinese pride, he was also mocking the Royal Society of Chroniclers of Florin.
ETA: (Sorry, my undergraduate class in Morgensterniana and the Academics sometimes comes back to haunt me.)
Brannaugh’s version is very faithful at many points, but it departs significantly in others, as many pointed out when it was released. (One of the points that bugs me was the implication, yet again, that something was wrong with the Creature’s brain – it’s shown getting severely struck on the heasd during its creation, just as the Hammer Frankenstein suffered bbroken glass i its brain. We’re no longer ijn the realm of “abnormal brain – do not use!”, but films frequently still see the Creature as damaged for some reason). I, by the way, was the one above that mentioned Brannaugh’s version, which I admire, but it still isdn’t completely faithful.
Much more faithful is the Per Oscarson Victor Frankenstein, which was made precisely to try and do a faithful version, and predates Brannaugh’s. You might also look at the more recrent William Hurt/Donald Sutherland version.
Two recent ones that were very faithful:
Life of Pi the only deviation being time-necessitated trimming. I do wish they’d kept the scene from the book where the Hindu priest, Catholic priest, and imam get into an argument but I thought Ang Lee deserved his Oscar for it in general.
The Hunger Games- again, trimmed some back story from an already slim book, but very true to the original material. They actually scrapped one of the most terrifying scenes from the novel after they began filming it- it’s the one in which Katniss realizes the “Mutts” have characteristics of the dead contestants because they decided it would be too expensive for something the audience might or might not notice without spending more time on it. Plus, that part was never actually explained in the book, which is one thing that made it so scary.
Going back to the '90s, Mother Night is religiously true to the original novel as you’ll ever get for a Kurt Vonnegut book, about the only straying being that Nick Nolte was a bit older than the character from the novel. Though the makers of Slaughterhouse Five did probably as good a job as possible.
I remember watching *The Quiet American *shortly after I’d read the book and being struck by how well the atmosphere and pacing of the book was caught. Recently re-watching, I did not appreciate the movie as much anymore for some reason (maybe because I’d already seen it; or because of Brendan Fraser? Who knows) but I still remember seeing it at the time and particularly liking how well it captured the book.
I thought the movie version of Get Shorty was relatively faithful to the book.
I think the 1963 “Lord of the Flies” was very faithful to the book. I haven’t seen the 1990 remake.
I actually disagree. The book has a bitter edge, mainly due to the frame-story, that the film lacks.
Silence of the Lambs should be mentioned in this thread.
Shawshank Redemption is very faithful to the novella, excepting the idea of Red being a middle aged red haired Irish guy!
The 1978 version of The Four Feathers is a low-budget TV movie, but it is more faithful to the book than any of the theatrical films I have seen.
Up until the end, The Mist was line-for-line faithful to the story.
For The Turn of the Screw, the book and the movie (with Colin Firth) actually enhance each other. The book is told in first person by the governess, while the movie shows what happened at the end. When you take both of the versions together, you get this chilling sense of how “removed” the governess was from the last scene.
That’s because Blade Runner is:
A. More faithful to the themes of its source material than I, Robot,
B. From a more obscure source than I, Robot, and
C. Better.
I loved “Blade Runner”. I simply can not read “Do Androids Dream of Electric Sheep”, try as I might.
I barely made it through that book. I remember almost nothing of it.