[Rogue]

I guess I'll start. I would say a character is developed when you can have a conversation talk that character as if he/she were a real person.

For example, I could say :
"Michael tried very hard to lead a 'normal' life and distance himself from the Family (in both the literal and symbolic sense). He joined the army and attended college as a way to shield himself from his past. He promised his sweetheart that he was different from the others. However, when he saw his father helpless and in mortal danger, he saw it as his duty to do right by his family by comminting acts that he was otherwise morally opposed to. It was as if something was set off inside of him that he previously thought he could control. For the rest of his life, he suffered greatly because of the hole he dug for himself (and his family). He committed terrible acts throughout his life, and although he somehow rationalized them enough so that they could be committed in the first place, he never truly convinced himself that they were right. Therefore, despite the enormous wealth and power he achieved, he never attained happiness. In fact, he lost what was most dear to him.
It was a shame for he was a natural leader, charming, and fiercely intelligent. Imagine what he could have accomplished if he directed his efforts towards something noble. What a waste."

I am of course speaking of Micheal Corleone from the Godfather trilogy. But notice how I just typed that from the top of my head without having to think too much about it. It was as if I knew this guy. Not only that, but most of you knew who I was referring to before I told you. That's how you know a character is three dimensional.
That is my meager attempt at a definition. I'm sure there is a 'textbook' version but I don't know it. For fun, try what I did with any character from a Steven Seagal or Jean Claude Van Damm flick (if you can remember any of the names) and see how far you get.

The depth needed for your characters can of course vary by genre. An action/adventure film doesn't need the same level as a drama. However, there is little excuse for complete shallowness. Even in an "blockbuster" type film, you have to know enough about someone to care about what happens on screen. But having said that, it is unfair to say that "Raiders of the Lost Ark" is a bad film because Indy isn't as well developed as Michael Corleone.

I think a lot of movies are unjustly accused of having two dimensional characters because the viewer simply isn't looking in the right place.
In novels and in theater, characters are brought alive differently. A novel has the advantage of simply telling you what is going on in someone's head and where they're coming from. In the theatre you can have monologues to achieve this. Films rarely have this luxury.
I think sometimes people are to quick to say 'film X has no character development', simply because they weren't told what they felt they needed to know. But since this is primarily a visual medium, one cannot limit their understanding of a film like that. Rather, ask yourself, "what was I shown?" Meaning that in movies, a facial expression or action can deepen our understanding of a character as much as a novel's long winded paragraph. You just have to work a bit and look for it.
Dialogue is only one (and often the laziest) way to do it. In fact, a script that spends far too much time telling us what someone feels or why they do what they do is often a weak one.