"Oh, I wouldn't read that if I were you," said the manager lightly, looking to see what Harry was staring at. "You'll start seeing death omens everywhere. It's enough to frighten anyone to death." (4.1.28)
Do you happen to be paranoid that people are actually out to get you? In Harry's case, the paranoia is probably justified, but the novel seems to indicate that paranoia in general is a problem. See Trelawney's obsession with death omens, or Snape's willingness to see conspiracies everywhere due his long-festering hatred of Lupin and friends.
Harry lay listening to the muffled shouting next door and wondered why he didn't feel more scared. Sirius Black had murdered thirteen people with one curse [...] But Harry happened to agree wholeheartedly with Mrs. Weasley that the safest place on earth was wherever Albus Dumbledore happened to be. (4.3.49)
Harry is probably experiencing some degree of shock here – he wonders why he isn't afraid, which implies a sort of detachment from his own feelings. But he also uses his unwavering trust in Dumbledore to combat his fear.
No, in all the thing that bothered Harry most was the fact that his chances of visiting Hogsmeade now looked like zero. (4.3.51)
The Hogsmeade field trip plotline is probably the most normal in the entire book. The novel overall deals with some dark stuff – murder, imprisonment, death, traumatic memories, and so on. But the Hogsmeade stuff really helps to show Harry's age. Instead of being concerned about the lunatic killer coming to get him, Harry focuses on a different kind of fear: the fear that he won't get to go to Hogsmeade like "everyone else."
"I'm not trying to be a hero, but seriously, Sirius Black can't be worse than Voldemort, can he?"
Mr. Weasley flinched at the sound of the name but overlooked it. (5.35-6)
The recurring fear most people express upon hearing Voldemort's name really indicates just how terrifying Dark Lord was and still is to the wizarding community.
And then the thing beneath the hood, whatever it was, drew a long, slow, rattling breath, as though it were trying to suck something more than air from its surroundings. (5.166)
Dementors are freaking scary. The detail about the "breath" here hints at the idea of a "death rattle" or the type of breath a dying person might take. Dementors are frequently described as "sucking" things like happiness and hope out of their surroundings. We just like how the notions of "sucking" something reminds us of leeches or parasites. And fear itself is parasitic, in a way – it attaches itself to someone and "sucks" away all good feelings. Hence, Dementors are the personification of fear itself.
"It was horrible," said Neville, in a higher voice than usual. "Did you feel how cold it got when it came in?"
"I felt weird," said Ron, shifting his shoulders uncomfortably. "Like I'd never be cheerful again [...]" (5.193-4)
J.K. Rowling has said that Dementors kind of personify depression, which helps explain the reactions that Neville and Ron have here. Rowling describes depression as: "that absence of being able to envisage that you will ever be cheerful again. The absence of hope. That very deadened feeling, which is so very different from feeling sad" (source).
"The charm that repels a boggart is simple, yet it requires force of mind. You see, the thing that really finishes a boggart is laughter. What you need to do is force it to assume a shape that you find amusing." (7.2.37)
That cliché about laughter being the best medicine really is true here. Lupin notes that the anti-boggart charm requires "force of mind," which is interesting. Fear is a largely internal, mental thing that an individual has to fight with his or her own force of mind.
Neville looked around rather wildly, as though begging someone to help him, then said, in barely more than a whisper, "Professor Snape." Nearly everyone laughed. Even Neville grinned apologetically. (7.2.45)
The details about Neville are really vivid here. We can actually see how scared he is, as he looks around desperately before answering Professor Lupin. As Neville demonstrates, sharing your fears can be really embarrassing. So what do you think of Professor Lupin, for making the entire class essentially share their deepest, darkest fears?
But before he had even started to plan a possible counterattack on a boggart-Voldemort, a horrible image came floating to the surface of his mind [...]
A rotting, glistening hand, slithering back beneath a black cloak [...] then a cold so penetrating it felt like drowning [...] (7.2.59-60)
Harry demonstrates a lot of maturity here with his choice of a fear. See, Ron's boggart becomes a giant spider, since he's "afraid" of them. But there are definite levels of fear, and Harry's fear, which literally rises up out of his subconscious, is of an abstract concept (fear itself), something an adult and not a kid would probably be most afraid of. Hermione, too, with her fear of failure, taps into this darker side of growing up, where you stop being afraid of monsters hiding under your bed and start being afraid of things like emotional experiences.
"I see," said Lupin thoughtfully. "Well, well [...] I'm impressed." He smiled slightly at the look of surprise on Harry's face. "That suggests that what you fear most of all is – fear. Very wise, Harry." (8.4.53)
See, Lupin totally agrees with us. Harry is very wise for his age. Being afraid of fear, of how it makes you feel and of what it can do to you, is pretty smart.
After about a minute inside it, she burst out again, screaming.
"Hermione!" said Lupin startled. "What's the matter?"
"P-P-Professor McGonagall!" Hermione gasped, pointing into the trunk. "Sh- she said I'd failed everything!"
It took a little while to calm Hermione down. (16.2.12-5)
We love seeing the form that Hermione's abstract fear of failure takes in her boggart. The fact that Hermione, one of the most logical people in the Potter-verse, completely shuts down when confronted with her own "failure" reveals just how intense a fear this is for her.
At that moment, there was a creak overhead. Something had move upstairs. Both of them looked up at the ceiling. Hermione's grip on Harry's arm was so tight he was loosing feeling in his fingers. He raised his eyebrows at her; she nodded again and let go. (17.61)
The silent communication between Hermione and Harry throughout the novel is pretty interesting to watch – these two make really good crime-fighting partners (and partners in crime, for that matter). Hermione and Harry both show their Gryffindor sides here: Hermione is brave enough to release her death grip on Harry and head upstairs with him; Harry is a good enough leader in a crisis to take charge and calm Hermione down.
Pettigrew was muttering distractedly; Harry caught words like "far-fetched" and "lunacy" but he couldn't help paying more attention to the ashen color of Pettigrew's face and the way his eyes continued to dart towards the windows and the door. (19.112)
Peter's picture is probably next to "fear" in the dictionary. The details about his body language, his speech patterns, and the diction used to describe him, such as "ashen," create this ongoing portrait of fear.
Harry felt his knees hit the cold grass. Fog was clouding his eyes. With a huge effort, he fought to remember – Sirius was innocent – innocent – We'll be okay – I'm going to live with him –. (20.62)
The theme of fear is tied to the theme of memory here, with the idea that fear and other dark emotions can make you forget hopeful, positive things.
"An' now 'es out," said Stan, examining the newspaper picture of Black's gaunt face again. "Never been a breakout from Azkaban before, 'as there, Ern? Beats me 'ow 'e did it. Frightenin', eh? Mind I don't fancy 'is chances against them Azkaban guards, eh, Ern?"
Ernie suddenly shivered.
"Talk about summat else, Stan, there's a good lad. Them Azkaban guards give me the collywobbles." (3.79-81)
Stan is probably one of those people that have seen all of the Saw movies in theaters. He seems to relish the story about Black here, especially how frightening it all is. Contrast this to Ernie, meanwhile, who doesn't want to talk about Black and Azkaban precisely because they're frightening. People's reactions to fear can be as informative as what they fear.
[T]he magical community lives in fear of a massacre like that of twelve years ago, when Black murdered thirteen people with a single curse. (3.56)
This idea of "living in fear" really sums up the magical community. We can see evidence of this with how people react to hearing Voldemort's name. It's like a whole group of people collectively decided to deal with their fear by ignoring it, or by trying to at least.