Stannis is slumped against a tree, battle-worn and with a severe wound in his leg, when Brienne of Tarth finally gets her moment to confront him. She explains who she is, and why she is going to kill him. And then she offers him the chance of some final words. His response: Go on, do your duty. They may not be the words many would come out with, and are hardly the most famous of last words, but they are extremely Stannis-y. Of course, right when he is about to die, the thing he thinks of is duty. That is what is important to him, and he did his duty until the very end.