Alignment is useful as a shorthand for DMs. If my players try to make a truce with this type of monster, is it likely to keep its word, or would it be willing to betray them? Except as a very general guideline ("No, your paladin can't murder people in their sleep and take their stuff."), it's not something that player characters should have to worry about.
For the record, here's the definition of "lawful" and "chaotic" as per the third edition:
Law (or Lawful) is the belief that everything should follow an order, and that obeying rules is the natural way of life. Lawful creatures will try to tell the truth, obey laws, and care about all living things. Lawful characters try to keep their promises. They will try to obey laws as long as such laws are fair and just.
implies freedom, adaptability, and flexibility. On the downside, chaos can include recklessness, resentment toward legitimate authority, arbitrary actions, and irresponsibility. Those who promote chaotic behavior say that only unfettered personal freedom allows people to express themselves fully and lets society benefit from the potential that its individuals have within them.
Batman (I can't believe I'm doing this ...) has no problem lying to criminals and flagrantly breaks the laws when it's convenient for him to do so, but he usually keeps his promises. He's not irresponsible and doesn't seem resentful towards legitimate authority (but also has no problem ignoring it). To an extent, he probably believes that personal freedom trumps authority (i.e. if Gotham tried to outlaw pornography, it's hard to imagine Batman going from bookstore to bookstore beating people up), while also believing that some sort of moral order needs to be maintained. I think he's pretty clearly neutral good:
Someone who is neutral with respect to law and chaos has a normal respect for authority and feels neither a compulsion to follow rules nor a compulsion to rebel. They are honest but can be tempted into lying or deceiving others if it suits him/her.
Good implies altruism, respect for life, and a concern for the dignity of sentient beings. Good characters make personal sacrifices to help others.
edit: Jarmo, in relation to the above definition, I think you'll have trouble showing that a paladin committing genocide shows "respect for life, and a concern for the dignity of sentient beings." Of course, D&D has always been a little weird about that, so I suppose it's up to the individual DM. My good cleric tries to resolve situations with "evil" races peacefully (without a whole lot of success, it has to be admitted).