I will say it publicly that I'm a little, filthy book-addict! (Book-addict is a sick person who prefers to stay home with his perfect book rather than going out with friends, the person that adores the smell of a book's paper. Basically a book addict is a lot more, so let's go further. Well around there in high school came the book that thrilled us all the way down to our backbone. Our Sweet Harry Potter! To those who read the books, we love you 'cause we are too cool for school. To those who only watched the movies, we like u. As for those who neither read nor watched anything... pff whatevah!
The Howgarts is the most super douper boarding school in the world. If anyone disagrees to this state has to come out to say it now, otherwise silence forever! There was magic, I mean real magic and no stupid things like "I guess i have the sixth sense" and nonsense. To me Harry owes his enormous success to his vivid description and to the juicy n' catchy scenario. His films tried instead -unsuccessfully- to destroy the perfectly designed magic world that i have imagined. The bustling diagonal alley and the christmas decorated Hogsmith are so vivid in my mind that sometimes when I get bored I go and drink butterbeer with some really bad guys. And the Howgarts? Ooh I've explored all his chambers and halls a million times and now that christmas comes we sit around the fireplace in our dormitory and.... enough already!
Basically this is my very personal opinion on the matter. However, there may be more factors, which helped the spread of the "Harry Potter epidemy". Hmm let's see,we start with the 11-year-old orphan Harry (bad start) and his stay in an unpleasant family environment. He receives an invitation to attend the school of Hogwarts, so he runs away from his problematic relatives to fall on the school bullies (Malfoy and Co.). Not long after he learns about Voldemort (murderer of his parents and a phycho ). He also learns about a prophecy concerning him and Voldemort, only one of them will survive by killing the other one!
Let's go a little deeper. Even 10 years ago when the books were firstly published, let alone now, about half of marriages end in divorce in the U.S. and Britain (guaranteed sources) and this fact often means the beginning of anxiety and fear for the children. Their world collapses and then the Pandora's Box of their problems open. Let's go back to Harry. The wound is visible on each page and the reader shares with him his heavy load. Harry finds the warmth and love he was looking for to the magical world. The biological family which he never had, was replaced by the Weasley family. Ron Weasley (Rumpert, marry me!!) and Hermione Granger quickly become his friends, almost brothers. Unfortunately, he meets the last alive member of his family, the unstable and no good father-model, his godfather Sirius only to the lose him, another trauma. Anyway, there are many signs which indicate that Harry had serious phychological problems and a teenager such as Harry would commit sucide in a dull mugle world. Thats for sure!
Children who have experienced broken homes, for whatever reason, have lost to some level the of belonging somewhere and a sense of security, which are essential for a healthy grow-up. Harry Potter was lost after the death of his parents. Nevertheless he tries to recover with the help of his magical friends, even though he is to young to fight all alone. Just because Rowling's books are children's books and they don't contain romantic/sex scenes (i know, i know you wish they had a few), they don't mention directly the psychological problems of Harry. So maybe Harry is the character, with whom all those children without stable parenting role models can connect and rely on. He is a safe harbor for them, 'cause Harry knows their problems and understands them. So does the popularity of Rowling's books show the size of a problem that exists by all these wounded hearts that read them? It's up to you to answer!
(All pictures are from the "Harry Potter wiki" site.)