I have to say two things turned me off. First is the idiot reviewer on the front page who feels the need to use 70% of his review(even titled it "Eat Your Heart Out Naruto" -really subtle) to bash Naruto like some insecure 12 year old spoiled brat fan boy. Pathetic. The second was that it sounded like some Gothic action anime from others. However when I finally saw it I thought, meh, okay. However as it went on I got more and more drawn in.
The plot is simple enough to start:successful and brilliant student Light stumbles upon the Death Note, which will kill anyone who's name he writes down provided it's their real name and he knows his face. He experiments with it and sees that it's real. He plays with the other rules all the while killing other criminals and meeting up with the shinigami who wrote the death note. The deaths of these criminals does not go unnoticed as the renound and mysterious detective El is trying to discover who Light, under the name Kira, is. Whoever finds the other's identity first will win in this power struggle.
Like I said, the first episode is interesting enough. The story however develops and becomes better and more complex as it goes on. The moral ambiguity of the anime gives it a unique feel among others of it's kind. I was shocked to see a show like this under Shounen jump which usually host anime that combine strong actions scenes with a complex plot and character development. What we have here instead is an anime that dosen't have adrenaline pumping action scenes advancing the plot(not that there's anything wrong with that, in fact I enjoy that as well) but the proverbial chess game between Light and the police as Light becomes well aware the police are after him as he does everything possible to hide himself all the while continuing to do away with criminals at his whim.
Ryuk, the shinigami who follows Light, actually provies some of the comic relief of the show believe it or not. He's not over the top goofy by any means however if there's any laughs to be derived, it's usually from him.
Even if you're not a fan of Shounen Jump anime, you should give Death Note a try. It easily rivals the majority of thriller films. It is well worth your time.