WHY IS CAPTAIN AMERICA LAWFUL GOOD? Because as many times as Steve Rogers has been declared an outlaw, it has never stopped him from trying to work within the rules and laws of his country for the greatest possible good. Even in Civil War, he was fighting for the higher law of The United States Bill of Rights even as he was fighting against the laws regarding superhero registration.
WHY IS BATMAN NEUTRAL GOOD? Much as I know everyone would like to peg Batman as Lawful Good so he's a polar opposite of Joker and as many arguments as I've heard that Batman is a deep believer in order, despite working outside the law... sorry, Bruce has too much going against him to be Lawful. Not only because Bruce breaks countless laws on a nightly basis (breaking-in-and-entering, assault, driving an unregistered, uninsured and decidedly not street-legal vehicle... and the bit in The Dark Knight where he illegally violated millions of peoples' right to privacy to give himself radar powers) but because Bruce's concern for achieving Good is more important than the ideal of Law and Order.
Superman himself put it best in Kingdom Come - "When you take everything else away from Batman, you have a person who doesn't want to see people die." That's about as good a definition of Neutral Good as I've ever seen.
WHY IS GREEN ARROW CHAOTIC GOOD? Fights Evil? Check. Works outside the law? Check. Issues with anyone who thinks you need a badge or a uniform to do good? BIG OL' CHECK. Plus, he's basically Robin Hood. Everyone knows Robin Hood = Textbook Chaotic Good.
WHY ARE THE GUARDIANS LAWFUL NEUTRAL? While they were always supposed to be an organization concerned with keeping order and preserving life, the "Keeping Order" part of the equation has always been the greater of the two. You can see in numerous stories how they tolerate individual Lanterns breaking their rules and defying their direct commands about as well as a three-year-old who has been told they can't have a cookie. And with the new Alpha Lanterns (cyborg Green Lanterns created by combining Manhunter technology with live Green Lanterns) in Green Lantern right now, it looks like the New Earth Guardians are back in the habit of trading freedom for security.
WHY IS CONAN NEUTRAL? Aren't barbarians chaotic by their very nature? Not necessarily and certainly not by the D&D Rules, which only required a barbarian be non-Lawful. As many issues as Conan has with city men and their pointless rules, he has always been willing to put aside his dislike of people telling him what to do for steady pay. Chaotic types don't generally thrive in the military and Conan certainly did thrive while in the employ of various armies. He played the soldier just as much as he played bandit, suggesting he had no strong feelings on law or chaos, one way or the other. And he certainly made an honest attempt at doing the job well once he became a King, despite being totally unsuited toward the life of royalty.
WHY IS JOHN CONSTANTINE CHAOTIC NEUTRAL? I've seen several people argue that John should be Chaotic Good because he honestly does try to do the right thing, more often than not. This is true. But John generally does a lot of evil things to accomplish that good, including intentionally sacrificing other people and trafficking with demons. The fact that John tries to do the right thing on occasion is the only thing keeping him from being Chaotic Evil. But even ignoring the means John uses to bring about individual ends, John's personality is geared toward doing things without considering the eventual result. Even without his magic, the demons around him and the angels behind him, it is John's nature to lash out against the world and Authority with a capital A. He was a rotten kid who disrespected his father. He was a punk singer. And he once arranged for a paranoid anarchist friend to wind up on the mailing list of a conservative Church group, just because he knew he'd be freaked out by their pamphlet describing the evils of rock and roll, Ouija boards and video games. Why? Because he could.
WHY IS DOCTOR DOOM LAWFUL EVIL? Doom is a man of his word. He respects the rule of law, even when the law isn't his own. At least, when written properly he does. He's a member of the United Nations and takes his position as a world leader seriously. He honestly does seem to make an effort at providing for his people and trying to better the world, even if the inspiration behind his acts is to show how amazing he is. And for all the tricky-dicks who want to point out the laws he violates going after The Fantastic Four... well, guess what, by our rules he doesn't have to follow our rules! Diplomatic Immunity for the win!
WHY IS DEADSHOT NEUTRAL EVIL? Amoral mercenary who will take any job to kill anyone, no questions asked. Sure, he has a wife and a kid now... but his first response in dealing with the people threatening their lives is to shoot, shoot, shoot, shoot and shoot some more.
WHY IS THE JOKER CHAOTIC EVIL? Oh, come on! Do I REALLY need to explain this one? Go see The Dark Knight again...