It's always been my opinion that the D&D alignments as is really discourage players from being Evil. By that toke, I recommend everyone who hates D&D alignment to investigate the alignment descriptions found in Palladium's RPG line. They're all there, all nine of them, but explained in detail.
Now, in regards to D&D, I believe the law-chaos and good-evil axes can be explained as the "how" and "why" a character accomplishes a given task.
Given the princess scenario above:
a) a Lawful Good character will opt to rescue the princess because it's the right thing to do; she is held against her will by a (likely) Evil tyrant and Good people oppose Evil when able. The LG character may hire a crack team of professionals to lead, march up to the gates, break them down, and rescue the princess and any other slaves s/he may find, destroying altars to dark gods and ruining wizard labs as they go, in the name of King and country.
b) A Neutral Evil character is primarily concerned with his/her own well-being. The King hires this character and the character accepts out of personal gain (money). The NE character then weights risk vs reward, and know that he likely can't do it alone and recruits a crack team of professionals to assist him. The NE agrees that any valuable goods found will be distributed equally among the troops but he reserves the right to have "first dibs". The NE will assess all possible dangers and conclude that a clandestine entrance would be preferable but may not be possible. He leads his troops to the front door, tries and fails to open the gate quietly, and directs the goons to enter. He fights alongside them when necessary, but if things look too bad, he's not against a tactical retreat, leaving the goons behind to get slaughtered. The NE realizes that hiring another band will be too costly, so he returns to the city, swipes a signet ring from a local lord, and returns to the King explaining that the princess is dead. He collects his reward, and goes on his merry way.
c) A CE character will do whatever will serve him best. He agrees to rescue the princess, offers the promise of riches to anyone who will join him, and hires a crack team of professionals to join him. He marches up to the castle gates, kicks them down, and directs the goons to enter. He leads from the front, reveling in the wanton destruction and murder of the opposition. If one of the goons goes down, he helps him recover for sake of appearances. Once the princess is recovered, he decides that the tower is quite defensible and the princess isn't really going anywhere, so he decides to keep her around for a while and perhaps sire an illegitimate son or two. He tells the princess to keep the source of her child a secret or there will be consequences. To emphasize his point, he kills one of his hired goons and points out how easy it was to get to her in the first place. As time rolls on, the CE arrives at court, announcing his desire to wed the princess. The princess agrees out of fear for her life, and the web of deceit begins to spin inside the castle walls, ensuring that the CE will eventually earn the throne.
This got a little long... but I guess my over-exaggerated point is, alignment is only a descriptor of how and why a person will act in a given situation. An Evil campaign generally means that the PC's will prosper at any cost, and that they will be willing to take shortcuts and step on the toes/lob off the heads of anyone who opposes their goals.
