[Morthoron]

The Fellowship of the Ring, without a second thought. It captured Tolkien's narrative best (save for perhaps the ludicrous presentation of Arwen invoking the waters at the Ford of Bruinen -- sorry, the original plot where Frodo squares off alone against the Nazgul is far more chilling). Perhaps it mirrored the book better because of its more linear progression, but I firmly believe that the other two movies were lessened by Peter Jackson's hamhanded efforts to subvert the plot to his evil will (as if it were the Ring itself).

If you really parse out the scenes in each movie, it is the unadulterated dialogue (even where another character speaks the lines) and scenes from the original plot that outshine the reinvented and reconfigured sensationalizations and muddled reinterpretations that characterized the scripting of Boyens and Jackson. One finds themself saying over and over, 'Well, that wasn't necessary' (the defamation of Faramir and Denethor, the breaking of Gandalf's staff, Aragorn falling off a cliff and frenching his horse, Frodo breaking faith with Sam, the Elves appearing then disappearing at Helm's Deep, etc.), or "Well, that's plain silly" (Legolas's shield surfing, Legolas's trunk surfing, the green Scrubbing Bubbles scouring Minas Tirith, Frodo showing the Ring to a Nazgul in Osgiliath, etc.).

FotR has far less digressions and unnecessary filler than the other two movies, and I believe the acting (thanks to Sean Bean, Sir Ian Holm, Cate Blanchett and Sir Ian McKellan) is a cut above the other movies as well.