Quote 1
"…It warns in this book how unstable you make the rest of your soul by ripping it, and that's just by making one Horcrux!"
Harry remembered what Dumbledore had said about Voldemort moving beyond "usual evil."
"Isn't there any way of putting yourself back together?" Ron asked.
"Yes," said Hermione with a hollow smile, "but it would be excruciatingly painful."
"Why? How do you do it?" asked Harry.
"Remorse," said Hermione. "You've got to really feel what you've done. There's a footnote. Apparently the pain of it can destroy you. I can't see Voldemort attempting it somehow, can you?" (6.71-73)
The matter of exactly how evil Voldemort is – more evil than anyone else has ever been, apparently – is one of the most frightening things about him. As Hermione notes, it's unlikely that he'll ever feel any remorse for any of the terrible things he's done.
Quote 2
"'The Tale of the Three Brothers' is a story," said Hermione firmly. "A story about how humans are frightened of death. If surviving was as simple as hiding under the Invisibility Cloak, we'd have everything we need already!" (22.6)
Hermione's kind of right – and mostly wrong, given the events of the rest of the book. Her point about humans' fear of death is right on, though; we'll do anything to talk around, above, and through death and the threat of it.
Quote 3
"…I'm as hunted quite as much as any goblin or elf, Griphook! I'm a Mudblood!"
"Don't call yourself –." Ron muttered.
"Why shouldn't I?" said Hermione. "Mudblood, and proud of it!" (24.87)
Hermione shows her strength and her confidence in her own identity here – she's not ashamed of her Muggle background, and she knows that it makes no difference to her Wizarding abilities.