I believe one of the actors (I'm thinking Sean Astin) was once asked which film was his favorite. (Maybe it was Dominic Monaghan.) And he replied "That's like asking which child is your favorite?"
I think all three contain a scope of grandeur and wonder that surpass anything we've seen before. If hard-pressed, I would have to admit (based almost entirely on in-theater opinion just after the movie ended) that Return of the King is my favorite.
Fellowship of the Ring: Started us off, introduced us to the happy times before the Shadow clouded the sun. I think Amon Hen is one of my favorite scenes; it has the most close-up shots and quick-take action bits. (Many other battles used Massive technology, but I don't believe Amon Hen did at all.)
The Two Towers: Introduced us to Rohan, but also spent a whole lot more time in the dark. Helm's Deep was a great sequence, but somehow, I must admit that The Two Towers is on the bottom rank of all three. (Which is still pretty high...) I must vote TTT at least had the best beginning of them all.
Return of the King: The awe-inspiring conclusion which all the movies, characters, events, themes, plots, battles, story lines and music were leading up to. This was the first movie that ever inspired me to tears; the horns of Rohan, arriving to save Gondor. And then again when Aragorn leads his troops against the host of Mordor whilst Sam and Frodo are at Sammath Naur. Every moment of the film, from the horns of Rohan on (with the few pauses, such as the Last Council) were breath-taking, soaring far beyond the expectations already set impossibly high by the first two. The end too was flawless; a perfect way to conclude not just the film, but the trilogy.
Wow, I think I just talked myself into watching them again.