For a long time I've had my mind made up that J.K. Rowling's third installment in the Harry Potter series was my favorite. It's also the last of the books that I've read multiple times. When it comes to books 4-7, I've only read through them once. So my opinion of which is my favorite may change when I get back around to rereading those. As of now, however, Prisoner of Azkaban is still my favorite.
Harry is once again spending his summer vacation in the home of his aunt, uncle, and cousin, all of whom hate our young hero. After some understandably negative events involving Uncle Vernon's sister, Harry packs up his things and runs away from his home away from Hogwarts. But these are dangerous days for a young wizard as famous as Harry Potter to be running around on his own. A convicted murderer, Sirius Black, has managed to escape from Azkaban prison (the place where wizards keep their convicted bad guys).
No one knows just how Black managed to escape since he's the first to ever pull off such a feat. But he's out there, roaming free in the world, and he has a connection to Harry Potter. As the story progresses, we discover that Sirius Black was very close friends with Harry's father, James. Back in their school days, James and Sirius spent much of their time getting into trouble with two other friends, Remus Lupin (the current Defense Against the Dark Arts professor at Hogwarts) and Peter Pettigrew (believed to be one of Black's victims).
Once again, Harry, along with Ron and Hermione, do a great deal of snooping throughout the school year and discover the truth behind Sirius Black's supposed crimes and his escape from prison. Harry learns more about the kind of person his father was and what kind of friend he was to Sirius, Remus, and Peter. Harry once again shows what kind of character he has, as he is faced with a situation to exact swift revenge for the deaths of his parents, but instead chooses to show mercy. As seen in the previous books, this is one more thing that separates him from his enemy, Voldemort.
I can't quite put my finger on exactly why this is my favorite of the series. Maybe it's the introduction of Sirius Black, who turns out to be innocent of all the crimes of which he was accused, and turns out to be Harry's godfather. Maybe it's the introduction of Remus Lupin, a good man with a good heart but with the bad luck of having been turned into a werewolf. Maybe it's because this book involves a bit of time travel, which always makes things interesting, if confusing. Whatever the case, book 3 is still a favorite. But as I said above, that opinion may change once I've read through the latter books once more.