By day, I'm a domestic violence prosecutor. By night, I read romance to restore my faith in love, relationships, and humanity in general.
Prisoner of Azkaban is my favorite Harry Potter book. It introduces the pivotal characters Lupin, Sirius, and Pettigrew, all of whom were dear friends of Harry's father. We learn what the four friends -- Lupin, Sirius, Pettigrew, and James Potter -- were like when they were Harry's age, and we get much more insight into why Professor Snape is so unpleasant. Lupin is the first competent Defense Against the Dark Arts teacher Harry's class has had, and through him we finally get a sense of what that area of study is supposed to involve.
This is also the book where Harry realizes that Dumbledore doesn't know everything and can't fix everything. At the end, after telling him what they have learned about Sirius, Dumbledore believes Harry and Hermione when no one else does, but his belief isn't enough.
"But you believe us."
"Yes, I do," said Dumbledore quietly. "But I have no power to make other men see the truth, or to overrule the Minister of Magic...."
Harry stared up into the grave face and felt as though the ground beneath him were falling sharply away. He had grown used to the idea that Dumbledore could solve anything. He had expected Dumbledore to pull some amazing solution out of the air. But no... their last hope was gone.
Thus begins Harry's process of realizing the limits of Dumbledore's guidance: the Headmaster is an enormously wise and powerful wizard, yes, and he is and continues to be a huge resource for Harry in his quest to defeat Voldemort -- but ultimately that quest is Harry's alone, and Dumbledore's help will only get him so far.
Ultimately, I like this book best because it is the most tightly-plotted of the seven Harry Potter books, I think. The first three books are relatively short, and the last four are much, much longer. Some of that is because the stories get increasingly complex as Harry's quest advances, but some of it is also just ... stuff. (I suspect that, in light of J.K. Rowling's unprecedented success, editors might have given her leeway to ramble where a less experienced writer would have been advised to cut. For example: the hundreds-of-pages-long camping trip that Harry and his friends take in Deathly Hallows. *snore*) Anyway, Prisoner of Azkaban is beautifully constructed, to the point where every single thing that happens in it is somehow necessary to the plot (if not of this book, then of books to come). There is nothing extra. The story whips along, never slowing, never dragging, and it's an incredible ride.