Death Note

A god of death can kill anybody-provided they see their victim's face and are able to write their victim's name in the Death Note (notebook kind of thing).  Ryuk "a god of death" became bored of the shinigami lifestyle and seemed interested in seeing how a human would use a Death Note, and he drops one into the human realm. 

Yagami a high school student and is considered a prodigy stumbles upon the Death Note, and tests out the deadly notebook by writing a criminal's name in it.  After the criminal dies immediately following his experiment with the Death Note, Yagami is surprised and quickly recognizes how devastating the power that has fallen in his hands could be. 

So with this new power Yagami decides to kill all criminals in order to build up a brand new world where there is no crime, and also a world where all the people worship him as a god.  But it is quickly discovered that the police have indeed discovered a serial killer who is targeting criminals and they try to apprehend the culprit. The catch is that the investigators must count on the assistance of the best detective in the world (a young and eccentric man known only by the name L.)