In book 1 harry was just coming to terms with the fact that he was a wizard and what had actually happened to his parents.
by book 2 he was trying to come to terms with whether he had been put into the right house or not, and realising more about his connection with voldermort
book 3 saw him learning a lot more about his parents, and his heritage and his link with sirius (making him feel a lot more like he had a family)
book 4 made him realise how much he had to grow up quickly with the death of cedric and his introduction to voldermort again
book 5 he seemed to be a stroppy teenager (but with good reason). he went through a stage of feeling hard-done-by, and wondering why everything had happened to him and subsequently dealing with the loss of sirius
book 6 showed us the more mature harry learning to deal with his destiny and what he;s going to have to do. i think he showed real maturity when he listened to dumbledore when he said that no matter what harry had to keep making him drink that potion, and realised that no matter how hard it was to see him in pain it was for the greater good. book 6 by far showed my favourite harry