I must have read the trilogy three or four times since I was first introduced to it via The Hobbit back in grade-school. I am not a purist, but some of the changes Peter Jackson has made along the way weren't to my liking. For example, I didn't like the deviation in Faramir's character during the Two Towers, despite Peter Jackson's claim that he needed to create additional tension and discord beyond what Tolkien included.
The Return of the King has same flaws, but overall I thought it was a more engaging movie than the previous ones. Beware, there are a few spoilers ahead; obviously, most of the Slashdot crowd knows the story in the books, but what will follow should be considered a spoiler, as I am describing Jackson's adaptation of the book.
The movie opens at what I thought to be a strange spot - Smeagol's killing his friend for the Ring; why not put this in the first movie? I think this may have been foreshadowing one of the more prominent departures from the book: Jackson decided to increase the tension between Sam and Frodo over the Ring, with Golem playing on Frodo's Ring-induced distrust. This tension did exist in the book, but Jackson makes it more overt. Personally, I thought it was a little over the top.
Obviously, the book is too large to be made into even a three-hour movie, but I found that one large part is missing that I hoped would be covered: the Battle of Bywater. In the book, when Frodo, Sam, Merry and Pippin arrive back at the Shire, they discover that Saruman and his thugs have enslaved the Hobbits. I have hope that this may be added into an Extended-Edition (probably due out this time next year).
A good chunk of this movie is spent on the moments leading up to the battle, the battle itself, and the immediate aftermath. As a result, I noticed that there were a lot of speeches of the sabre-rattling kind made by principal characters that I'm sure weren't there in the book -- a kind of Holywood-ization in the Gladiator spirit. It probably makes the movie more interesting to people who haven't and won't read the book.
The humor that could be found in The Two Towers (specifically, Gimli) carries over into The Return of the King. I didn't mind the humor, though I know it's an addition that Jackson made.
Along the way, I noticed other small deviations, but I'll leave those for Tolkien fans to argue over.
Enough complaints; there were a lot of great scenes, and many of the plot lines were handled deftly by Jackson.
Shelob getting Frodo, and Sam taking him for dead, is done particularily well. Jackson didn't change much at all here, and the effects are great.
From the book, I remember a strong impression of bleakness as Sam and Frodo take the final stage of their journey to Mount Doom -- Jackson got that dead-on. Jackson does an excellent job showing the toll that the Ring is taking on Frodo.
The battle outside the walls of Minas Tirith puts the battle of Helm's Deep to shame. The high walls of the city built into the cliff, with a huge army of orcs outside the walls, have to be seen to be believed. I don't actually remember any in-depth description of the battle outside Gondor (in fact, I don't remember any great battle depictions from any of the books -- bad memory?), but Jackson does a great job of providing one. The trebuchets are particularily engaging.
Overall, I would have to say that this was my favorite of the three movies. The movie was a little more grim, a little darker, and showed some of the violence and fighting in a more disturbing fashion. I am hoping that some of what I perceived as shortcomings will be fixed in the Extended Edition (the Two Towers's Extended Edition was a much better movie that the theatre version). I can't wait to see it again.