Death Note
Light Yagami is an ace student with great prospects, who's bored out of his mind. One day he finds the "Death Note": a notebook from the realm of the Death Gods, with the power to kill people in any way he desires. With the Death Note in hand, Light decides to create his perfect world, without crime or criminals. However, when criminals start dropping dead one by one, the authorites send the legendary detective L to track down the killer, and a battle of wits, deception and logic ensues...
I highly recommend this. It will get you hooked with the good storyline right away. I saw the Japanese broadcast version of this last year and it still gives me chills to my spine (yes, it's that good).