Note: All quotes taken from pages in the American versions of the books. No quotes have been altered to fit the Harry/Hermione shipper perspective. Seeing [...] only means that I've omitted parts of text that have nothing to really do with the main point of the quote, or that the quote goes on for too long for our purposes.
Chamber of Secrets
Hermione is incredibly worried about Harry after Ron writes to tell her he's going to try and rescue him. In fact, her entire note seems like a long run on sentence of nervousness!
Harry is adamantly standing his ground with Dobby, despite the danger to himself. He's worried about Hermione. When Dobby mentions that the monster is attacking Muggle-borns, Harry doesn't worry about all his friends that are Muggle-borns, but rather Hermione alone. His first thought is of her.
Despite how much Hermione adheres to the rules, she volunteers to commit a pretty serious crime that could get her expelled because she doesn't want Harry to get in trouble, and because she knows how important this is. It proves how much Hermione cares.
Harry moved automatically toward Hermione.
"I don't think so," said Snape, smiling coldly.
There are other Gryffindors (or Hufflepuffs and Ravenclaws that Harry gets along with) in Snape's class that would have been fine to team up with. But Harry moves automatically to Hermione, as though his subconscious makes the decision for him. He doesn't want to be with anyone else.
Hermione automatically moves to help Hermione the second he sees she's in trouble. He doesn't care how much bigger Millicent was compared to his own size when Hermione was in pain. He also forgot about his own duel with Malfoy the moment he spots Hermione.
While Hermione tries to sound fine through the bathroom stall, and Ron doesn't notice, Harry knows something is off. He's concerned about her and wants to make sure she's alright, but he looks at his watch and sees they don't have time.
Professor McGonagall seeks out Harry, of all the people in the school, to bring to Hermione's side when she's petrified. When he sees her, he can't even speak. He just nods his head when McGonagall questions him and stares at Hermione.
Harry is so distraught over Hermione being hurt he can't even concentrate on what people are saying. He's extremely worried about her, about being sent home, about everything.
It's funny because everyone suspects Harry until Hermione is attacked, which seems to clear everyone's minds of the idea of Harry as the bad guy. It's like everyone knows Harry cares about Hermione, but they thought he was guilty when it was other Mudbloods. They recognize how close he and Hermione are and realize the moment she's attacked there's no way Harry did it. This is a great moment because it's not Harry or Hermione's actions that define it, instead it's everyone else's reactions.
The final line of the book, which may not sound like a Harry-Hermione moment to anyone but me, but I just love how this is phrased. As if they're some united front walking though fire together. I just figure there are a lot of different ways JK could have written this, and find it interesting that she chose those words. Like they're facing going home together. Aww!