I know, I'm two years late to the party, but I finally decided t see what the fuss was about. I became instantly hooked. And it's funny, because I usually like faster-paced anime with fights and all that crap, but this one doesn't have any of that. Rather, it's just a bunch of intellectual wars between the protagonist (who's also the bad guy) and the cop trying to catch him.
What it's about:
A seventeen year-old named Light finds a notebook that can kill anyone in the world who's name is written in it, as long as the person's first and last name are written in it, and his face is pictured in the mind of the person writing it.
He begins using the notebook to kill criminals all over the world. Eventually, people start noticing it, so the police hire a genius detective named L to find the teen ("Kira," the Japanese word for "killer," is the name given to him by the public). Thus begins the intellectual wars mentioned above.
L is the best anime character in the universe.
So yes, apparently not all anime is blood-and-guts crap.:D