In the books, it's written that Harry's hair won't lie flat, which I take to mean that it sticks up. On special occasions, he tried to make it lie flat, but its natural state was unruly.
I tend to picture this as looking like he has a
serious
cowlick in the back of his head. If that's not messy enough for canon, then my back-up image is that he looked like he's just gotten out of bed after his hair's gotten quite messed up in his sleep. So, for the most part, I feel that Harry's hair was a bit too tidy in the first two movies. There are a few moment when it looks a slight bit untidy on top, but it's not too noticeable. Hence, I don't feel it's as messy as canon says it should be.
In the third, it was a lot closer to canon, in my opinion, but it was a little too stylized, I felt. Harry never struck me as the type who'd spend time styling his hair. I think of him as the kind of boy who brushes his hair right after he gets up in the morning (or combs it right after his shower, whatever the case may be) and doesn't do anything else to it the rest of the day. In fact, the way I see it, if he was at the Burrow during the summer holidays, he might not even brush it until after breakfast, since he's not trying to avoid negative attention being paid to him (as he would at Privet Drive), and there are no teachers there to dock points for looking untidy. So, I thought that his hairstyle in the third movie looked like it required too much styling time and products. In canon, this is still the boy who wears Dudley's huge hand-me-downs when he's in Muggle attire. He isn't focused enough on his appearance to spend time on his hair. He accepts that he can't control it, and he moves on.
I personally hated his hair in the fourth movie, and it affects my enjoyment in watching that movie to this day. His hair isn't just unruly in that movie, it's
long
and unruly. That seems to be the style in that movie, though. Ron and the twins all have long-ish hair, and I think all four boys look less handsome because of it. It detracts and distracts from their good looks. I don't think that Molly would have let her boys grow their hair that long, either, not the sons who still lived at home especially. She lets Bill get away with it because he's the oldest son and of age, and she can't really force him to cut it (though she can repeatedly suggest that he
should
). But, she even cut Charlie's hair not long before Bill & Fleur's wedding (against his preferences), if my memory's correct. I think Charlie only submitted to that because it was a formal occasion, and I think his hair was needing to be cut because he'd been too lazy to do so and tended to focus more on his work than his appearance. So, he wasn't making a personal statement with his hair; he'd just let it go. But, I digress.
I personally loved Harry's hair in the fifth movie. It looked great on him. It also made him look older than he had in the fourth movie, and I think of that as a good thing, story-wise. In
Order of the Phoenix
, he's starting to think less like a boy, and more like a young man. Also, in this movie, his bangs (or fringe, I guess it would be called) more or less covers his scar, which would be something Harry would try to do, in order to try to minimize being recognized whenever possible. Even though I think his hairstyle isn't as messy as canon says it should be, I also try to qualify it as having been cut so short because Harry was trying to keep the messiness factor under control. One point I'm thinking about: in this movie, he's wanting to date Cho, so he might have learned that he ought to work a bit harder on his appearance, in that case. Hence, shorter hair would be easier to keep tidy.
I know, I put way too much thought into this discussion point, but it hit a nerve with me, since I can't stand his hair in the fourth movie. Sorry I went on so long.