Quotes I can easily remember are mostly from Call of Duty Modern Warfare 2, such as the infamous announcements in online multiplayer such as:
ENEMY AC-130 ABOVE!! The spetsnaz say it with such emotion compared to other teams as well as announcing that a nuke is imbound, it sounds like their sobbing.
Uncharted 3 when Drake is scaling a Mountain with his female friend (forgot her name), she climbs up above him, he looks behind him and says 'Nice view'. The girl scoffs and says 'Men...' :P
Assassins Creed II, after Ezio makes his first assassination (not the first guard you kill), he shouts and mentions that the auditore line isn't finished, he remains. ''I am Ezio!, Ezio Auditore Da Firenze!''
Also, from a short film called Assassins Creed Embers, this quote stood out to me. "When I was a young man, I had liberty, but I did not see it. I had time, but I did not know it. And I had love, but I did not feel it. Many decades would pass before I understood the meaning of all three. And now, the twilight of my life, this understanding has passed into contentment.
Plenty more, but those are all I can think of for now.