It is really good thus far. I am not deep into it yet, but I already see the potential. The gist of both the manga and anime is that a god of death is bored so he drops his death notebook into the human world, just to see what happens. The rules of the notebook are: if the holder of the notebook thinks of a person's face while writing that individual's name in the notebook the person will die 40 seconds later of a heart attack. The writer must think of the person's face to prevent people with the same name from dying. The writer can go on to write details on how he/she wants the victim to dye including time and manner of death.
The main character finds the notebook and after becoming convinced it works, begins a crusade to purge the world of evil by literally killing off all bad people he sees online and on the evening news. His goal is to create a world in which only good people live, and bad people are too afraid to hurt others. More and more, he views himself as a god to purge the planet of evil so that a new society can form.
What is so interesting about the series is how it is a deeply moralistic play. You can easily read it as just an interesting story, but you can't help wondering if the characters are "good" people or not. It isn't realistic (obviously) and the police are searching for him using a mysterious uber-detective named "L" who seems just as fanatical as the main character. The both believe they are absolute justice: that they, and they alone, are the sole arbitrators of safety and shepherds of order. Pretty deep and intense stuff!
It reminds me of Socrates' ring of invisibility story in which two philosophers argue about if any man was given a ring that could make them invisible would he remain a good person. One argues that without consequences for his actions he would become a monster, the other argues that there is an intrinsic goodness about man. The Death Notebook is a similar item. The series stresses that anyone that found it would be tempted to use it, even if it was for altruistic purposes such as helping terminal patients who wish to die do so with dignity, or, as the protagonist uses the book, simply stopping the worst criminals. Yet at the back of the series is the constant question of the righteousness of the actions, the morality of killing. By stripping away any real consequences (he believes he cannot be caught, and he does not even have to kill anyone only write their name) the series cuts to the very essence of the morality of murder.
This kid isn't spiderman or batman - he does not do what he does because he is trying to stop a crime that he never can. There is no reason for him to do try and cleanse the world of evil, other than he thinks the world is "rotten". He is more like Superman, fighting to make the world better because of his own beliefs. He is more of an idealist than most "heroes", yet, he kills and is a megalomaniac. The series is shaping up to be a very dark look at vigilantism and a complex moral universe that American authors are too timid and rarely tackle.
I simply love these kinds of moral plays! Which is why I love Japanese literature so much.