1. The first time Snape speaks to Harry, he asks, "Potter! What would I get if I added powdered root of asphodel to an infusion of wormwood?"
2. In Philosopher's Stone, the Weasley twins managed to hit Quirrell in the back of the head with snowballs.
3. The entrance to Dumbledore's office...
4. Many believe Hedwig's namesake Saint Hedwig is the patron saint of orphaned children.
5. Sirius is not just your favourite; he was also the favourite of the Greek gods.
Whereas Albus has Latin origins: It means "white", perhaps for his beard.
6. Most people have noticed by now that Diagon Alley is a play on the word "diagonally".
7. In Chamber of Secrets Harry found himself in Borgin and Burkes, and "looked around quickly and spotted a large black cabinet to his left..."
8. Ron's Patronus is a Jack Russell terrier.
And who happens to have an otter Patronus?
9. In Prisoner of Azkaban, Professor Trelawney refuses to sit at a table with Dumbledore, as 12 people already sit.
In Order of the Phoenix, Sirius is the first to stand at a table of 13.
After the Battle of the Seven Potters in The Deathly Hallows, only 13 made it to the Burrow.
10. Speaking of numbers, seven is a fairly important one in the Harry Potter series.
11. And while we're on the topic of seven, each Horcrux was destroyed by a different wizard or witch.
12. When Harry and Dudley are attacked by Dementors at the beginning of Order of the Phoenix, Harry struggles to explain what Dementors are to Uncle Vernon.
"They guard the wizard prison, Azkaban," said Aunt Petunia.
Two seconds of ringing silence followed these words before Aunt Petunia clapped her hand over her mouth as though she had let slip a disgusting swear word. Uncle Vernon was goggling at her. Harry's brain reeled. Mrs. Figg was one thing - but Aunt Petunia?
"How d'you know that?" he asked her, astonished.
Aunt Petunia looked quite appalled with herself. She glanced at Uncle Vernon in fearful apology, then lowered her hand slightly to reveal her horsy teeth.
"I heard — that awful boy — telling her about them — years ago," she said jerkily.
Harry assumes Aunt Petunia is talking about his father, James, but then in The Deathly Hallows, we discover she got this information from Snape.
"Tell me about the Dementors again"
"What d'you want to know about them for?"
"If I use magic outside of school -"
"They wouldn't give you the Dementors for that! Dementors are for people who do really bad stuff. They guard the wizard prison, Azkaban, you're too—"
He turned red again and shredded more leaves. Then a small rustling noise behind the bushes made him turn: Petunia, hiding behind a tree, had lost her footing.
"Tuney!" said Lily, surprise and welcome in her voice, but Snape had jumped to his feet...
13. In Half-Blood Prince when Harry sees Dumbledore's memories, he sees Voldemort ask for a job at Hogwarts.
In The Deathly Hallows, of course, we find out who that local barman is.
14. Back to Trelawney and her seemingly terrible divination. In Prisoner of Azkaban, she says to Harry...
Harry tells her he was born in July, making her intuition seem way off base.
15. In Harry Potter, a Squib is a magic-born person with no magical abilities.
16. The Marauders died in reverse order from the order in which they are named on the map: Moony, Wormtail, Padfoot, and Prongs.
17. In Goblet of Fire, Harry and Cedric take the portkey to the graveyard, where there is a large yew tree near Tom Riddle Sr's grave.
18. The "Dark Mark" given by Voldemort to his Death Eaters is a skull with a snake tongue.
When the Basilisk first emerges from the mouth of Salazar Slytherin in Chamber of Secrets...
19. In Goblet of Fire, Harry and Ron make up predictions for their Divination homework, inadvertently predicting exactly what will happen to Harry in the Triwizard Tournament.
Harry's first task was to face a dragon and risk being burned alive, then he lost a treasured possession when Ron and Hermione were taken and put in the lake.
20. Then there is this earth-shattering theory of the books...
21. Finally there's Natalie McDonald, the only real person to be included in the Harry Potter books.
Bonus: Google "wingardium leviosarr."
H/T to this Quora thread / Mugglenet.
Harry's wand, as correctly pointed out by a powerful witch or wizard in the comments, was made from Holly. The Muggle who wrote this post accidentally said that Harry's wand was also made from Yew.