To get away from the do what you want sort of thing. I wanted to talk a little bit about three flavors of the alignment you often see in literature, more specifically A song of Ice and fire.
The Liberator: In this case you have a character that is actively working against some evil of oppression, in many cases slavery. Here you have a character with a clear opposition to something bigger than himself. He is often working to root our slavery or injustice where he sees it. This is perhaps the version that is nearest to Chaotic Good. A big difference is the Chaotic Neutral character is less a freedom fighter and more someone who reacts to oppression when he sees it. He may have a campaign against slavery but does not care for the people he has freed. In A Game of Thrones Daenerys Targaryen.
The Free Agent: This character is out for himself. This can be a mercenary that changes sides based on the highest bidder or a warrior who abandons a lord when the battle goes against they. They are not a coward they are often just not concerned with anyone else and wont be bothered by others suffering. This would certainly be The Hound Sandor Clegane in A song of Ice and Fire.
The Loon: There are some characters that are just crazy. These character are loose cannons who perhaps view themselves as doing the right thing. These are often the most fun characters to have in the group as they often ruin every ones well laid plans. They will also ruin the Game Masters plans as they often will left when the games goes right, dragging the entire party with them. They are often not leaders but create a huge shift that completely redirects the storyline. In combat they are usually the most heroic character around, actively seeking deadly situations. In a game of thrones the resident Loon is Lyssa Aryn