Light Yagami is the antagonist of the story by definition because he kills people on his won judgement, outside the rules of the law.
(Even a criminal could have his side of the story. And maybe, just maybe, no matter how disgusting the crime of the criminal, he/she had a reason behind the actions.)
Light Yagami, not the villain, because he chooses and kills criminal who have escaped the law due to the lack of evidence. etc.
No, no, no, Light is the
protagonist "villain". There's a difference between an antagonist and a villain, you know. The protagonist is the main character in the story whom deals with obstacles (conflict, antagonists, etc.) and the one the story revolves around. A hero is someone who fights for a "good" cause and tries to save people/justice.
Without Light, the story wouldn't take place, so you can presume he is the protagonist. L, the Task Force, and anyone else who gets in the way, are antagonists, because they interfere with what Light, the protagonist, is trying to do. Even Wikipedia says Light is the protagonist and L is the main antagonist!
http://en.wikipedia.org/wiki/List_of_Death_Note_characters
Yes, hero and protagonist are usually correlated, but they aren't always mutually inclusive. I hope that makes sense.
(Also, like Nico was saying, there's not actually a true "villain" and "hero" in Death Note, as it is left to the viewer to decide, but I think Light is portrayed as the villain and L is portrayed as the hero.