The first Planet of the Apes (1968) film had one for Charlton Heston's character. After recovering from being shot in the throat, the intrepid space captain escapes into the city, where he's subsequently caught in a large net, in town square. The first words the apes ever hear from a human throat? "Take your stinking paws off me, you damn dirty APE!"
The ending certainly has to count as one, as it's perhaps the most famous Downer Ending for a Hollywood blockbuster. And Heston plays it for all its worth: "Oh my God... we finally, really did it. You maniacs! You blew it up! Ah, damn you! God damn you all to hell!"
In Escape from..., Doctor Zira easily solved the intelligence test set for her by the human scientists, then refused to eat the reward which supposedly motivated her: "Because I loathe bananas."
Which are (chronologically speaking) the first words humans ever hear from an ape throat.
Even better, rather than using the blocks to build a tower and then climbing it (what the scientists expected her to do), she uses them to build a staircase, and then calmly walks up it.
The entire creation of the planet of the apes in Conquest, ending with a plea from Caesar that they prove themselves better than their human oppressors, and "We who are not human can be humane."
Galen from the TV Series got one when a human was planning on using gas bombs first to wipe out the apes who'd been oppressing his village, then to wipe out all apes everywhere. The human had said, "As long as it won't kill my people, nothing else matters." The normally quiet and gentle Galen then picks up a big stick and knocks him out in one blow, saying, "He won't kill my people either."