The Magical Signifigance of the Number Seven (7)

In Harry Potter and the Half Blood Prince, it is revealed by Tom Riddle that the number seven is the most powerfully magical number. Because of this, Tom Riddle decides to create six Horcruxes, instead of the usual one, dividing his soul into seven pieces. The number seven has also been used several times throughout the books:

Hogwarts requires seven years of schooling before graduation, and it's also the number of books in the series.
The Weasley family has 7 children, in which Ginny Weasley is the seventh child and only daughter.
Harry Potter is born in July, the seventh month of the year.
In the game of Quidditch, there are seven players.
If you add the numbers of Platform Nine and Three Quarters (9 3/4): 9+3+4=16, 1+6=7.
Hogwarts has 142 flights of stairs: 1+4+2=7
Gryffindor Tower, the Headmaster's office and the Room of Requirement are on the 7th floor of Hogwarts.
There are 700 different fouls in Quidditch.
Throughout the series, Harry and Dumbledore have been together in a Pensieve seven times: once in Harry Potter and the Goblet of Fire, and the other six in Harry Potter and the Half-Blood Prince.

In Harry Potter and the Philosopher's Stone:
Gryffindor has not won the house cup for seven years.
Nicholas and Perenelle Flamel have a 7 years age difference.
Harry has to overcome 7 obstacles to reach the Philosopher's Stone: Fluffy, Sprout's Devil's Snare, Flitwick's flying keys, McGonagall's giant chess set, Quirrell's troll, Snape's potions puzzle and the Mirror of Erised. The potions puzzle features seven bottles of different shape each and a riddle.

In Harry Potter and the Chamber of Secrets:
Hogwarts' students have to buy all the 7 books of Gilderoy Lockhart.

In Harry Potter and the Prisoner of Azkaban:
The Marauders' Map shows seven secret passageways that go to Hogsmeade.
When Sirius is caught, he is held in Flitwick's office, which is in the seventh floor.
Hermione says that there are only 7 registered Animagi in the last century.
In the film, Harry wears the number 7 in the Quidditch match.

In Harry Potter and the Goblet of Fire:
Frank Bryce is nearing his 77th birthday.
Harry arrives to the Quidditch World Cup at seven past five.
There have been 421 Quidditch World Cups before the one in the book, and 4+2+1=7.
The first Triwizard Tournament was held 700 years before the events in the book.
Fred and George charge 7 sickles for each Canary Cream.
Moody's trunk has 7 locks, and Moody was locked in the seventh lock.

In Harry Potter and the Order of the Phoenix:
Mrs. Number Seven looks out of the window when Mundungus Fletcher Disapparates while guarding Harry.
Clause Seven of the Decree for the Reasonable Restriction of Underage Sorcery states that an underage wizard or witch can use magic either to save himself or to save someone else, be it Muggle or wizard.
When Molly Weasley is facing the Boggart at Grimmauld Place, it has seven different forms.
Lily and James began dating in their 7th year at Hogwarts.
When they go to the Department of Mysteries to save Sirius, Harry and the DA, seven rooms are mentioned.
When Harry falls into the Death Chamber, seven people came to his aid: Neville, Sirius, Remus, Kingsley Shackelbolt, Tonks, Moody and Dumbledore.

In Harry Potter and the Half-Blood Prince:
Harry is waiting for Professor Dumbledore since seven o'clock in the evening.
The Ministry of Magic sends a leaflet with seven ways to protect the home and family against Dark forces.
Harry and Ron receive each 7 O.W.L.s.
Blaise Zabini's mother has been married and widowed seven times.
When brewing the Draught of Living Death, the Half-Blood Prince potions book says to "add a clockwise stir after each seventh counterclockwise stir".
When Harry hides from Professor Trelawney, she is reading tarot cards. One of them is the seven of spades, an ill omen.
During his private classes about Voldemort, Harry sees seven different memories.

In Harry Potter and the Deathly Hallows:
When disguising Harry by creating copies of him, they decide to make six copies (the chapter in which this happens is called "The Seven Potters").
In the British edition of the book, the Ministry is said to have fallen in page 133 (1+3+3=7) and the first kiss between Hermione and Ron happens in page 502 (5+2=7).
Although Voldemort decided to make only six Horcruxes to divide his soul in seven parts, there are seven Horcruxes in total (Tom Riddle's Diary, Marvolo Gaunt's ring, Salazar Slytherin's locket, Helga Hufflepuff's cup, Rowena Ravenclaw's Diadem, Harry and Nagini). Each of them is destroyed by a different person (Harry, Dumbledore, Ron, Hermione, Vincent Crabbe, Voldemort and Neville, respectively).