OK, many Potter fans have deep criticism for the Prisoner of Azkaban movie because of various scenes and details excised from the book. Also they get all riled up at the way Hermione is portrayed by Emma Watson as more of an all-action beauty than the geeky-but-loyal book version. Well frankly all of this is so petty it's ridiculous.
This was the one that brought the Harry Potter movies out of the whole kids-flick category and into something much more interesting. For the first time we get a REAL movie rather than sections of the book cobbled together and forced onscreen like the first two were. It's stylish and contains performances with real emotion and integrity, particularly in the scenes between Harry and Lupin, and finally scenes with the young actors that didn't feel like kids in a play. Everything is much more natural and less cliched. Sadly some of this adaptation-by-numbers routine returned in Goblet of Fire, which is why Azkaban is still my favourite (though Goblet is still great).
I must mention John Williams's score which is incredible, one of his best ever which is a feat in itself considering his massive body of work including Jaws, Jurassic Park and the Star Wars series. The main 'Window To The Past' theme is so beautiful and perfect for Harry Potter. I really hope Williams returns for later movies as he couldn't do Goblet of Fire due to Revenge of the Sith commitments.
Anyhow, if you only want to watch one Harry Potter movie then this is it because it stands on it's own and you don't really need to know what happens in the first two.