*** SPOILERS ***
#1 - TRUST - I used to tear my hair out whenever Harry could and should clearly tell somebody like Dumbledore about whatever crisis he's in, and he never does. He always tries his best on his own, usually with the help of his friends. I want to scream "Tell an Adult!" Of course, by the 2nd or 3rd book, I had figured out that Harry simply does not trust adults and has good reason for it. One natural outcome of the abusive treatment by his aunt, uncle, and cousin before age 11 is not trusting people, and specifically adults. It still drives me batty, even with that understanding. I even worried about young readers thinking they should rely on their own abilities instead of adults. I can only hope that children who have trustworthy adults will know when and how to open up to these adults. Perhaps they learn (through Harry's story?) who is worthy of their trust. SO, in Deathly Hallows, trust is an issue over and over again for Harry. MILD SPOILERS HERE: Harry worries about trusting adults in the Order and even his closest friends. Lupin reminds Harry about the dangers of trusting the wrong people.
#2 - IDENTITY & CHARACTER - Harry's character is fairly well established, as we have seen his choices and actions, and is reaffirmed in Book 7. The message of "you define your own character" is reaffirmed with Harry, Snape, Regulus & Sirius Black, Tonks and her mother, and others. Even mistakes are part of the process of defining character. Dumbledore is one example of someone whose early missteps and subsequent choices all define the person's identity. Harry passes this message to the next generation.
#3 - PARALLELS to our world - social class struggles, discrimination, prejudice. Wizards vs. goblins/elves/other creatures vs. muggles compared to racial, cultural, socioeconomic, gender, etc. conflicts in our world. Reminds me of Wicked by Gregory Macguire.