Oh, man, where do I even start?
Pretty much everything that came out of Dak's mouth in HBC. I can almost recite a few of his 'speeches.' The way he talked about his people was so heartfelt and moving, and even though you already know what happens to the Hork-Bajir, you just can't help but to desperately root for them anyway.
The line "Be happy for me, and all who fly free" from #3. That one always sends chills down my spine, because I think it's probably the one time that Tobias actually admits to being happy.
Elfangor's line "Out of a respect for life, you have to endure" from book #33.
And, obviously, what other people have said. The end of the books, when everything was going to hell in a handbasket, was a very emotional time for all of us readers.