I never find it easy to say what my favourite anything is, book, film, scene, whatever.
So I'll just mention one which I'm surprised hasn't appeared on this thread yet:
–the Balrog scene in Moria. The creature doesn't look like the one in the book, but it's a great monster, anyway. And I like the lead-up to it– you know, where the Orcs surrounding the Fellowship hear the Balrog coming and suddenly melt away?
(Admittedly, I could have done without the dopey dwarf-tossing joke a bit later.
)
Also, I like the battles in general and just about anything featuring those spectacular rapid camera-sweeps.