One of my favorite 'serious quotes' is at the death of Theoden in RotK when he says "I go to my fathers, in whose mighty company I shall not now feel ashamed."
Then two more serious quotes are both by Aragorn in RotK. The famous "My friends...you bow to noone" at Minas Tirith and his speech at the Black Gate.
"Hold your ground, hold your ground! Sons of Gondor, of Rohan, my brothers! I see in your eyes the same fear that would take the heart of me. A day may come when the courage of men fails, when we forsake our friends and break all bonds of fellowship, but it is not this day. An hour of woes and shattered shields, when the age of men comes crashing down! But it is not this day! This day we fight! By all that you hold dear on this good Earth, I bid you stand, Men of the West!"