Death Note
Death Note is a 2006 anime about an intelligent teenager named Light Yagami who finds a death note on the ground. The death note has the power to kill anyone if you write their name and think about their face. Many people would not use this power, but Light decides that he needs to use it to kill criminals, ending crime once and for all. He has gained all of this power through the death note, and feels that he is responsible for stopping crime. He thinks that the crime system is broken, so he thinks that he has to save the world by killing the criminals. Later on in the series, he is able to rid the world of many criminals and the crime rate goes way down due to the fear of being killed if you commit a crime.
Light Yagami
However, Light has some people who don't agree with his philosophy. The police want to find him, but they don't know who he is because he does not have to be at the crime scene to kill anyone. Enter L, one of the smartest detectives in the business. His philosophy is different than Light's. He thinks that it is the responsibility of the police to get criminals and put them in jail. Ultimately, it is up to the viewer to decide which philosophy is correct, but it is clear to see that Light believes that he is responsible for "cleaning" the world of criminals. The show does an excellent job of making you choose who is correct, and never outright says which one to choose.
L