The Dursleys had ignored his last two birthdays, and he had no reason to suppose they would remember this one. (1.26)
This sentence pretty much sums up Harry's experience with the Dursleys and clues us in to the awful people that they are.
"As I expected!"' said Aunt Marge, taking a huge swig of brandy and wiping her chin on her sleeve. "A no-account, good-for-nothing, lazy scrounger who –"
"He was not," said Harry suddenly. The table went very quiet. Harry was shaking all over. He had never felt so angry in his life.
"No, Vernon," hiccuped Aunt Marge, holding up a hand, her tiny bloodshot eyes fixed on Harry's. "Go on, boy, go on. Proud of your parents, are you? They go and get themselves killed in a car crash (drunk, I expect) -"
"They didn't die in a car crash!" said Harry, who found himself on his feet. (2.3.17-21)
As we discover in this book, nothing sets Harry off as fast as a disparaging remark about his family. We also love the irony of Aunt Marge dissing James for being a drunk loser while she herself is getting pretty wasted and belligerent at the moment.
"I notice they haven't made you two prefects."
"What do we want to be prefects for?" said George, looking revolted at the very idea. "It'd take all the fun out of life."
"You want to set a better example for your sister!" snapped Mrs. Weasley.
"Ginny's got other brothers to set her an example, Mother," said Percy loftily. [...]
He disappeared and George heaved a sigh.
"We tried to shut him up in a pyramid," he told Harry. "But Mum spotted us." (4.2.86-9)
The interactions we see in Weasley clan are the best examples of family dynamics in the entire book.
Mrs. Weasley kissed all her children, then Hermione, and finally, Harry. He was embarrassed, but really quite pleased, when she gave him an extra hug.
"Do take care, won't you, Harry?" she said as she straightened up, her eyes oddly bright. Then she opened her enormous handbag and said "I've made you all sandwiches [...] Here you are, Ron [...] no, they're not corned beef [...] Fred? Where's Fred? Here you are, dear [...]" (5.24-5)
Mrs. Weasley is definitely the mother figure of the book, and is really the sort of mom everyone wants – loving, considerate, and strict (hey, it's a good thing sometimes).
Percy Weasley (acting, Harry suspected, on his mother's orders) was tailing him everywhere like an extremely pompous guard dog. (9.2.5)
Percy shouldn't pursue a career as a spy. Details like this really emphasize how Harry is basically a part of the Weasley clan now. And they look out for their own.
Everyone said the Dementors were horrible, but no one else collapsed every time they were near one. No one else heard echoes in their head of their dying parents. (10.1.4)
Harry's status as an orphan is central to his character. Others define him as such, and Harry, interestingly enough, is fixated on his parents death himself. This has a lot to do with how they died, of course, and it's also worth remembering that Harry only learned how they died two years prior, in Book 1. He hasn't had much time to come to terms with that yet.
"Your mum and dad wouldn't want you to get hurt, would they? They'd never want you to go looking or Black!"
"I'll never know what they'd have wanted, because thanks to Black, I've never spoken to them," said Harry shortly. (11.2.27-8)
This is a really tense scene and we can see how Ron and Hermione are out of their element here. They don't really know how to talk to Harry or comfort him about his parents. This is partly why the introduction of Lupin and Sirius in this book is so important – Harry also needs some adults he can confide in and talk to.
"And the Acid Pops? Fred gave me one of those when I was seven – it burnt a hole right through my tongue. I remember Mum walloping him with her broomstick." Ron stared broodingly into the Acid Pop box. "Reckon Fred'd take a bit of a Cockroach Cluster if I told him they were peanuts?" (10.3.93)
Ah, sibling rivalry. Thankfully, none of our siblings burnt a hole in our tongues with acid. We don't actually see Ron interact with his brothers a ton, even though they attend the same boarding school. But whenever they do interact, they're usually teasing or fighting – so, typical sibling antics.
"Potter trusted Black beyond all his other friends. Nothing changed when they left school. Black was best man when James married Lily. Then they named him godfather to Harry." (10.3.145)
The detail of Sirius becoming Harry's godfather represents how friends can become family over time and particularly as you grow up. We can already see this happening with the trio, who manage to survive a year of almost non-stop arguing and still emerge on the other side of it all as stronger friends.
Rage such as he had not felt since his last night in Privet Drive was coursing through him. He didn't care that Snape's face had gone rigid, the black eyes flashing dangerously.
"What did you say to me, Potter?"
"I told you to shut up about my dad!" Harry yelled. (14.3.75-7)
Great callback to the night Harry blew up at his aunt for shooting her mouth off about his family (and blew her up too, for that matter). Given how Harry's parents were practically martyred in the war with Voldemort, it's no wonder that he's overly-sensitive to any insult dished out at them.
It was a stag. It was shining brightly as the moon above [...] it was coming back to him [...]
It stopped on the bank. Its hooves made no mark on the soft ground as it stared at Harry with its large, silver eyes. Slowly, it bowed its antlered head. And Harry realized [...]
"Prongs," he whispered.
But as his trembling fingertips stretched toward the creature, it vanished. (21.301)
This is definitely the emotional climax of the novel. The anticipation builds up, and we get the sense Harry is holding his breath, until Prongs finally vanishes. The detail about Harry's trembling fingers is really powerful too.
"You know Harry, in a way you did see your father last night [...] You found him inside yourself." (22.3.56)
Leave it to Dumbledore to perfectly sum up a theme for us. Dumbledore is saying that the people we've loved and lost are still a part of us. So Harry still has his parents with him after all.