"Tom Riddle" and "Lord Voldemort" have 7 syllables altogether.
If the letters of the alphabet were turned into numbers (A=1, B=2, etc...), the letters in the name Harry would add up to 70. (8+1+18+18+25=70)
If the letters of the alphabet were turned into numbers (A=1, B=2, etc...), and added together until a single number is found, as done in Arithmancy, the letters in the name Harry result in the number 7. (8+1+18+18+25=70, 7+0=7)
"Bridget" and "Wenlock", the first and last names of the person who established the magical properties of seven, both contain seven letters.
Voldemort made seven Horcruxes, even though he believed that six Horcruxes would create a seven-fragment soul (including the piece of soul in his body). The singular of Horcruxes (Horcrux) is seven letters long.
During Harry's hearing in the Ministry (in 1995), Dumbledore states that clause 7 of the Decree for Reasonable Restriction of Underage Sorcery allows the use of magic in life-threatening situations.
Behind the scenes
The first book was released in 1997, and the final book was released in 2007.
The epilogue itself is set in 2017.
Many fans expected Harry Potter and the Deathly Hallows (the seventh book) to be released on 07/07/2007, which also happened to be a Saturday, the day upon which Harry Potter books had previously been released. However, it was released on July 21st of that year instead, two weeks later. It is thought that the more 'magical' date was rejected due to it also being the second anniversary of the 7/7 London Bombings in 2005. (21 is still a multiple of 7 though.)
The number on the back of Harry Potter's Quidditch robes in the films is seven (this could be a reference to the fact that usually the best player/captain in a football team, has the number 7 shirt).
J. K. Rowling stated in interview that she chose to write seven books in total because she spent seven years in secondary school. Also, she wanted Harry to come of age at seventeen because it "just seems a good number for a wizard to come of age."
In the seventh Harry Potter book, J.K. split the dedication in seven parts.
There were seven clues and seven opportunities to sign up and register for the Pottermore beta. The first clue was on 31 July 2011 (Harry's birthday) and the final was 6 August 2011. A clue was released each day and each clue was from a book in the series corresponding to the day. For example, day one's clue was from Philosopher's Stone and the final clue was from Deathly Hallows.
↑Wonderbook: Book of Potions - The first Championship was known held in 1407, which is a multiple of seven. Since the event was held every seven years, unless there were irregularities, every subsequent Championship was also held in a year divisible by seven.