The scene where Gwaihir rescues Gandalf from Orthanc

Boromir's last stand

Entire battle of helms deep, especially when the elves arrive

Charge of the rohirrim (Both helms deep and pelennor)

Boromir's last stand at Amon Hen defending Merry & Pippin

The charge of the Rohirrim at Helm's Deep & Pelennor Fields

The self-argument/torment between Gollum/Smeagal

The Council Of Elrond

Boromir's war-cry atop the towers of The White City.

I assume you're thinking EE (Extended Edition).

Well,if I start counting my favourite scenes,I 'll stop typing tomorrow!So ,I say only two of them,just for sentimental reasons:

• The stew scene in TTT(EE).Just watching the expressions of the always-too-serious-Aragorn makes me burst to laughter!(and it happens rarely with me)
  
• The beacons of Amn-Din.Outstandig photography,epic music that brings me tears,Denethor's face:D(though they are too many,Gwathor,indeed.Anyway,they are made only of wood,so lets make some more,it makes impression:p)

#1 Frodo leaves for the Undying Lands ...no words to explain why. All the actors perform beautifully.
#2 Gandalf comes back! While watching the film, I jumped, saying, "He's back! Yay!!!" :D
#3 Pip's song.
#4 Sam carries Frodo!
The list is endless, so I'll stop now. :D

Haldir's death, thereby rectifying that which never should have been.

The whole Black Gate Opens scene was really well done, even though most of the dialog was invented for the movies, I've no difficulty with it and think it's at least true in spirit to Tolkien's intentions. So Aragorn's "A day may come" speech, Legolas and Gimli ("side by side with a friend") and the final "for Frodo..." are high up there in my own "moments of awesome" list.