This topic was actually fairly difficult for me. I love Harry Potter, if not for the genius that is J.K. Rowling and her marvelous ability to turn a plot, then for her awesomely believeable yet magical characters. In other words, I have many "favorites", but these two stand out:
Rubeus Hagrid. The Keeper of the Keys and Grounds and Hogwarts :) Rubeus Hagrid is one of my favorite characters, for starters, because of his unbending loyalty. I am not surprised at all that he was originally sorted into Gryffindor, where dwell not only the brave at heart but also the just and loyal. He willingly puts his life on the line for those who have shown him kindness, and to those he feels the need to protect. It all seems to start with Dumbledore. Because Dumbledore showed Hagrid the ultimate kindness of keeping him on as gamekeeper after he was expelled, Hagrid would do anything for him. For instance, when Dumbledore asked him to please bring the infant Harry Potter to Privet Drive, he jumped at the chance. Not only did Albus Dumbledore ask him for assistance, but he also knew that there could be a baby in trouble, and a baby who was the offspring of two other people that he admired. And don't ever think of insulting Albus Dumbledore in front of him. He may just turn your kid into a pig =P
Another reason that Hagrid is one of my favorite characters is his comic relief. Hagrid is morbidly hilarious because of his love for all things dangerous. What makes it even more funny is that Hagrid legitimately doesn't see how dangerous most of the creatures are. He hatches a baby dragon in his hut and keeps it there, convinced that Norbert will be safe even though he's very quickly outgrowing the place and slowly demolishing it from the inside out. He was expelled from Hogwarts for a similar reason when he harbored a deadly Acromantula in the castle. Granted, he was expelled because he was framed by Riddle, but still, he shouldn't have been keeping that creature in the castle. He also brings dangerous and unsettling creatures into his Care of Magical Creatures classes - Blast-Ended Skewts, Hippogriffs, and Thestrals come to mind. Students often don injuries as a result. I can sympathize with Hagrid on this because I often feel that people look at me funny when I watch a shark attack a seal and exclaim, "Look how COOL!" I mean, I feel awful for the seal, of course, but in general, the more dangerous it is, the more I'm going to think it's awesome. It's good to know someone else like that exists, even if he's fictional.
Draco Malfoy. Ah, the class asshole. Everyone knew one in school, and for Harry, it's the self-important, arrogant son of the even more self-important and arrogant Lucius. I did a paper studying Draco's character for our HP class with Dr. Diehl, and one of my topics was the reasons why Draco became and stayed such a jerk throughout his seven years at Hogwarts. The first reason was his parents. They let him get away with anything, indulged his every whim, and treated him as if he was a gift to the entire world. The result was a child who expected others to treat him in the same way. When Draco then arrived at school, he found Crabbe and Goyle, who took all of Draco's crap and acted exactly as he wanted them to act - like his lackeys. No one in Slytherin - the only group of people whose opinions Draco really valued - gave him any reason to not act the way he always had growing up, so why should he stop? When he saw that Harry Potter - another young wizard of fame - was nothing like the way Draco thought he should be (i.e., like him), yet still gets attention, Draco retaliates with bullying and derogatory remarks. I think Draco is fascinating. From the first time he walked into the book in Madame Malkin's Robes for All Occasions, I hoped that we would see more of him. I love a character in need of redemption :)
HAPPY BIRTHDAY, HARRY POTTER!