I have written about this in the past (especially in my old "blog" at my homepage), but I think it deserves repeating.
There isn't a single movie that properly captures the essence of Batman in the comics (at least not any professionally-made big-budget one.) The only non-comic artwork that I have encountered that really captures this spirit is the Batman: Arkham Asylum and Batman: Arkham City video games. They are dark, gritty, violent and badass... yet they still somehow retain the kind of "innocence" of the comics' world. The characters feel like the characters of the comics, and the entire setting and atmosphere feels like the ones from the comics.
In my opinion, not a single movie has ever succeeded in doing this. So, what do I think of Christopher Nolan's Dark Knight trilogy?
The first movie follows a rather clear three-act structure, not only in its contents, but also in its quality. The first act (which shows Bruce Wayne's background) is good (not perfect, but good), the second act (which shows how he builds the character of Batman) is mediocre, the third act (the battle against his foes) is just horrendous.
And I will never get tired of repeating this: They never get, and will probably never get, Batman's costume right. In all movies it has been just horrible, and the first movie in the trilogy is no exception. They clearly take the "knight" part way too literally. Batman should be an agile "ninja" that looms in the dark, disposes enemies without them even noticing, and instilling uncertainty and fear. He's not supposed to be a soldier in full body armor that looks more like a black Michelin Man than a ninja. That's not Batman. That's someone else.
The second movie was overall much better, and consistently good. Batman was not really the Batman of the comics, and especially the Joker was most certainly not the Joker of the comics, but it wasn't a bad movie at all. It's just that you have to consider an alternative universe of sorts, a universe with clear and drastic differences from the universe of the comics. A "parallel universe Batman" of sorts. (Batman's costume got an upgrade that made it better, but it's still not Batman's costume. It's something else entirely.)
The third movie is... just underwhelming. Dull. Plodding. It clearly tries to be deep and epic, but in the end that just feels hollow. Any "depth" feels forced and tacked on. The best way to describe it is as if it was something like "Batman's mid-life crisis." Exactly as thrilling and interesting.
I have to go against the majority here and consider the entire trilogy quite underwhelming. It's something that clearly tries very hard to be very deep, epic and larger-than-life, but in the end all that feels just like an empty shell with no actual substance. The second film is enjoyable, but that's about it. It's the only one I would watch again, and I wouldn't even bother with the other two.
And even at the risk of sounding like a broken record: This is not Batman. This is something else. It might resemble Batman a bit, but it's not. It's a parallel universe Batman that's not the real McCoy. It just isn't.