What quote from Lord of the Flies depicts courage?

Piggy makes a bold stand of courage just before his death. For the duration of his existence on the island, he is cast aside from acceptance by most of the boys. He is ridiculed for his weight and asthma and used because his glasses provide fire for the group. Piggy is unwavering, however, in his commitment to trying to preserve order so that the group doesn't devolve into chaos. And in his final scene, Piggy is seen standing defiant of all that Jack represents:

“I got this to say. You’re acting like a crowd of kids.” The booing rose and died again as Piggy lifted the white, magic shell.
“Which is better—to be a pack of painted Indians like you are, or to be sensible like Ralph is?”
A great clamor rose among the savages. Piggy shouted again.
“Which is better—to have rules and agree, or to hunt and kill?”

In this scene, Piggy stands utterly alone in his convictions, booed by the boys and viewed as a "bag of fat." Yet he does not give up. He boldly proclaims the worth of the leader they previously elected and thereby the flaws in Jack, the leader they have now chosen to follow.

This takes great courage, and it is significant that it is Piggy's final act. Immediately following, a large rock descends on Piggy, killing him and shattering the conch which he's so desperately tried to hang on to.

Courage is revealed when a person does something that usually makes him or her afraid but which he knows will serve a greater purpose and so he does it anyway. In Lord of the Flies, there are various displays of courage. Courage is shown by Piggy when he realizes that Ralph needs his help in making rational decisions. Piggy is afraid of Jack but still tries to stand up to him, even if it is the conch that makes him feel brave. Just before he dies, Piggy makes a valiant attempt to get his glasses back and to try and restore order- "to have rules and agree" (ch 11). Even though the other boys often belittle him and snigger at him, he tries to stand his ground, with tragic consequences.

Ralph is courageous in accepting the role of chief and even though he questions his abilities later, he still tries to keep order. Ralph consistently reminds the boys that shelter is important, water is needed and a fire for rescue is crucial even though this makes him unpopular sometimes. When Jack tries to take over, Ralph reminds Jack that he is chief, even though he is in territory which Jack has claimed. This also shows his tenacity and reveals his courage.  Even at the end, Ralph accepts responsibility and makes the ultimate display of courage when the naval officer asks who the "boss" is and Ralph does not hesitate in volunteering himself. Jack makes no such show of courage or offer to share the blame for what may have taken place on the island in the absence of "grown ups" and he stays quiet.

Simon is courageous and faces his fears when he confirms that the beast is not real. It is just a "pig's head on a stick" (ch 8). Simon wants to warn the others and "walked with a sort of glum determination..." (ch 9). His efforts will cost him his life. 

A quote that expresses the courage that all three boys display is found in chapter 5 when Ralph is preparing for the evening assembly:

He found himself understanding the wearisomeness of this life, where every path was an improvisation and a considerable part of one’s waking life was spent watching one’s feet...There must be no mistake...no chasing imaginary..."

Ralph has realized how difficult it is keeping order and yet he forges on, doing his best and showing a strength of character and an understanding that "you had to be wise..." 

This quote from chapter 8 demonstrates that courage is a transient thing for the boys, and depends on circumstances.

The book depicts a group of boys isolated on a deserted island by a plane crash with no adults.  They have to find their own way, and they begin to recognize the danger lurking among them. It is a metaphorical danger, but it manifests itself in the symbolic danger of the beast.

The boys are concerned with the beast even though they are not sure what it is.  It is a manifestation of their fear and insecurity.  They can feel it closing in on them.

“As long as there’s light we’re brave enough. But then? And now that thing squats by the fire as though it didn’t want us to be rescued—” (ch 8) 

By now, the breakdown of society is almost complete.  The boys are breaking into two camps and are acting like heathens, right down to war paint and dances around the fire.  There is plenty to be afraid of, but the danger lurks in their own hearts.

Which three situations or characters in "Lord of the Flies" illustrate courage in adversity?

The boys who crash land on the island in Lord of the Flies face a great deal of adversity, and some of them display a significant amount of courage as they do so. Simon, Piggy, and Ralph are the boys who exhibit courage to the greatest degree. Simon has the best insight about the beast. Knowing that the thing the boys really have to fear is each other, he tells Ralph during their search of the island, "I don't believe in the beast." This gives him courage, after his terrifying interaction with the Lord of the Flies in his vision, to climb the mountain by himself to discern exactly what Samneric saw. He sees "a humped thing suddenly sit up on the top and look down at him," but he keeps climbing until he reaches it. Despite the disgusting condition of the decaying body that causes him to vomit, he cuts it loose and then goes back to the boys, desiring to tell them the good news. Going on this lone mission, he displays more courage than the other boys who observed the fallen paratrooper.

Piggy, after his glasses have been stolen, has the courage to confront Jack with his crime. Although he has known for some time that Jack hates him and that Jack is dangerous, he still insists on confronting Jack face to face to demand his glasses back. He shows great courage in speaking truthful accusations to Jack and his tribe. Unfortunately, in his nearly blind state, he is unable to see the oncoming boulder soon enough to save himself, and he is killed by Roger. 

Ralph also shows courage. Like Piggy, Ralph is willing to confront Jack and demand he return Piggy's glasses. He, too, calls Jack out on his wicked behavior. Despite his fear, he manages to get information from Samneric as they guard the fire, and later, although he is in a state of panic, he shows courage by not giving up but by fighting back against those who are hunting him.

Simon, Piggy, and Ralph are all commendable for the courage they show.