PJ already mentioned it himself : with this movie he allowed himself to add more bits and pieces of himself and be less faithfull to the book. This is very true but (and that's a big BUT) it all is done in such a way that the essence of the story remains true to what Tolkien wrote.
TTT immediately blasts off with an jawdropping opening sequence. At first, all is quiet. Then you hear some familiar phrases... And then... WOW !
The movie switches back and forth to Frodo and Sam, Merry and Pippin, and the pursuers Aragorn, Gimli and Legolas. Most of the time is spent with Aragorn and his companions. In TTT more empasis is laid on the fact that Aragorn still has to earn his throne and to do that, he has to become a true leader. That also means to sometimes support one who appears to be not that good a leader himself and/or to go against the odds and hope for the best. This ofcourse reaches it's climax at the battle of Helm's Deep which is just awesome. A true epic battle which exceeds my wildest dreams.
The story of Frodo and Sam (and Gollem) gets a fair amount of time and attention. Gollem is a completely convincing character (well done indeed Andy!) and one of the most notable additions to the cast besides being a top CGI. Expect a few smiles and jawdrops from him. Their encounter with Faramir could have done with a little more 'as told in the book' but it is not rushed story. Just shorter than I would have liked it. Then again in my opinion even the extended DVD cut of FOTR is too short.
Considerable less attention receives the story of Merry and Pippin which is a shame in my eyes. But seeing as what their part is in the book and taking into account the starting and ending point of the movie it is understandable. (Hopefully the extended DVD cures this a little.) Also, a last comment. A lot of scenes and phrases that appeared in the trailers have not made it to the final movie cut. I know this happens a lot but a lot of these scenes I thought would have been sort of necessary. Hopefully they will re-appear in the extended DVD-cut so that, as with FOTR, it will make for an even better movie.
In short : TTT is a blast that will have your ears and eyes ringing for some time. It is more overwhelming than FOTR mainly because of the fabulous battle at Helm's Deep. Which almost makes one guess that ROTK will be even more awesome. Go see this movie ! Again and again.