Spoilers The Theme Purists Review... - This was better than I thought would be possible.
I liked the dynamic development of Faramir instead of the static iconization he gets in the book. We get the same Faramir in the end (i.e., wise enough to do what his brother could not), but Faramir cannot simply refuse the Ring straight up. We need to see what convinces him that it is a curse rather than a blessing, and the whole Osgilliath sequence did that beautifully. It also made Faramir intermediate between Boromir and Aragorn instead of Aragorn-lite. (Given that Aragorn was tempted in the movie, unlike in the book, we need to see Faramir struggle more than Aragorn to refuse it.) Also, it makes Faramir's choice in the end (the hard, self-sacrificial choice) more obvious than in the book (where there was a vague possibility of trouble). That is, after all, the story in a nutshell.
I liked the development of Gollum as a full-fledged schizophrenic, with a remnant of Smeagol pining for companionship struggling with Gollum for control. I actually fond him completely pitiable and his fall will seem all the more tragic for it. They dropped his aversion to the light, but that is a necessary sacrifice for cinematography. Also, the light = good versus dark = evil contrast no longer reflects modern morality and is best dropped.
Also, having Frodo overtly take on some of Gollum's characters and needing to think that Gollum could be saved develops this aspect of Frodo more fully than the book did. Too many readers fail to appreciate just what happens to Frodo and I think that it is critical to the story to show Frodo being destroyed. Showing him caressing the Ring and eyeing it as his precious does this perfectly. His attempt to reveal himself to the Nazgul emphasizes this further. Sam's part is done perfectly here, as he can better recognize the effect of the Ring while at the same time failing to appreciate what the Ring does to a bearer. Sam's little speech at the end borders on over-the-top but really summarizes the why of the story perfectly. In other words, I really liked the character development Sam, Frodo and Smeagol/Gollum receive - obviously, it goes further than the book and thus might not be what Tolkien intended, but that was his fault, not Jackson's. The close, with Gollum winning and Sam and Frodo wondering about their place in history, was perfect.
The Rohan sequence was wonderful. Merging Erkenbrand (a non-character of no importance) with Eomer removed one character from the clutter and provided a more obvious cavalry to come to the rescue. (OK, that hill was a little steep for horses, but I'll give them some lee-way). Eowyn was perfect, as was Wormtongue. I loved the exchanges between Eowyn and both Wormtongue & Aragorn that used dialogue from RotK. This develops Eowyn's character now, as opposed to after her main deeds. It also made Wormtongue look extremely perceptive as well as just plain evil. Her interactions with Aragorn are perfect - she clearly is infatuated whereas he is somewhere else.
Gimli also gets some good development, especially in his exchanges with Eowyn. The part about dwarvish women was wonderful and I like the humor he injected (gods, it was needed). Plus, his fighting was awesome. Tolkien's weak development suggests a sleepier Gimli, but I like the bombast. Legolas' fighting was, too, even if he is no longer the hottest chick in the movie. I wish that they could develop a character for him, but Tolkien left even fewer clues for him than for Gimli. And, there simply is not time.
The Elves at Helm's Deep was fine. I liked seeing them do something, and it eliminates the question so many readers have of why the Elves did nothing. (They did, but it is documented only in the Appendices.) Adding Dol Guldur complicates things too much, so having them realize that they need to aid men even though they have not done so in so long was fairly moving.
My one qualm with the movie was with how the Ents decided to go to war. It actually is not much different from the book - the Ents see that Saruman is destroying their forest and decide to go to war. However, by having it be a spontaneous reaction rather than a deliberated one, the choice seems less self-sacrificial. (I realize that it really is not, but it is a timing-thing). Also, it just did not quite look right - Treebeard howls and suddenly a bunch of ents turn up, ready to fight. Now, I realize that this was done in part to give Pippin a moment of insight to inspire Treebeard onwards. I suppose that this might have been done before the Entmoot, but this would have deprived Merry of the scenes where he exhorts the Ents to fight, which show him to clearly grasp the situation (and, as always, faster than Pippin to do so). Keeping to the book would have lost the character development, so I suppose this is a fair trade-off.
In short, this is what you want a movie adapted from a book to do - emphasize the primary theme (here, individuals realizing that the obvious "safe" choices lead to ruination and the only hope lies in nearly hopeless choices) while attempting to correct the weaknesses of the original book (e.g., the lack of character development, failure to adequately use characters, etc.). This did as good a job of that as I can imagine.