Regarding both the films and the books (can't reallycomment on the books as I've only read fotr this past month and just started ttt), which battles, duel, charges and any other moments worth of awe inspiring action are your favourites and most memorable.
for me I have a few, my favourites being that of the members of the fellowship against againast all the gribblies and beasties they have to face, from the eerie watcher in the water, to the Mighty and terrible Balrog, right down to Sam's heroic stand against shelob.
from these i would have to pic of course, the Balrog as i i haven't seen any other duel of the like, and the first memory i have of wathcing the film and seeing Gandalf hold back the Balrog of Morgoth kept me at the edge of my seat for the whole duration... also like how it concluded in the next film as Gandalf slew the Balrog at the the top of the Misty mountains on the ruins of Durins Tower.
coming in second and very closley would be the first sight of a troll, another scene in Moria where the Feloowship are beset by Goblins, which had a cave a troll, and seeing the cumbersome beast destroy the burial chamber and all about him in a primitive ferocity and finally alsmot impaling the ringmearer with a spear.
lastly the Last March of the Ents, a wonderful part of the ttt where the ents of Fangorn led by treebeard, bring down the walls of Isengard and imprison the wizard Saruman for his treachery. some great scenes like the ent using the orcs as a weapon, and of course the breaking of the damn and the flooding of isengard.
there are many more I am also keen of such as the storming of the gate of minas tirith where th trolls rampaged through the first line of defenders. The charge of the Rohirrim, both at Helms deep and at the pelennor, and of course the counter charge of the titanic Mumakil.