A couple of you hit it right on the head. The following is from a web chat with J.K. Rowling on Bloomsbury.com last year.
Quote:
Twinkletoes: Why did you feel that Hedwig's death was necessary?
J.K. Rowling: The loss of Hedwig represented a loss of innocence and security. She has been almost like a cuddly toy to Harry at times. Voldemort killing her marked the end of childhood. I'm sorry... I know that death upset a LOT of people!