There exists a world other than this one, in which creatures called Shinigami (lit. "gods of death") live. Each shinigami has a notebook that he carries around with him, called a Death Note. With a Death Note, it is possible to kill anyone as long as you know their name and face, simply by writing their name in the book. It's also possible to specify the time and circumstances (as long as they're possible) with the Death Note; not doing so causes a death by heart attack.It's not too often that you see a anime or manga series centered around a full-on antihero—usually the closest you get is an "antisocial hero", tragic hero, or sympathetic villain. But Raito is the real deal: although he starts out ostensibly to "create a better society", his "ends justify the means" attitude borders on the sociopathic, and he's soon "sacrificing" innocent people (some of whom you get to know and like beforehand) to protect himself and feeling less and less remorse. Ryuuku is no help; he's basically amoral, and concerned mainly with his own entertainment. L, our antagonist, is to a degree sympathetic but, well, kind of strange.
One shinigami named Ryuuku, bored with his world, accidentally-on-purpose loses his Death Note (complete with instructions) in the human world, where it's found by a brilliant high school student named Yagami Raito. Raito discovers its power, and decides to clean up the world by eliminating all of the bad people (criminals in particular). Ryuuku, who Raito can see because he touched the Death Note, tags along as a sort of observer (but not exactly ally).
Rumors begin to circulate that the unexplained rash of heart attacks among criminals is due to some sort of god, which people start calling Kira. Interpol, alarmed (but conflicted) by these strange events, assigns their best detective to the case, a mysterious man known only as "L". With Interpol, the police, and others investigating, Raito starts to kill to keep people off of his trail. Soon it's turned into a game of mutual cat-and-mouse, with Raito and L each trying to uncover the other's identity in order to stop him, without revealing his own...
While it's presented as a shonen manga (it originally ran in Shonen Jump), there is very little overt action as you'd expect, especially as it involves death and supernatural powers. But the Death Note's ability to kill at a distance means that most (but not all!) deaths occur "off screen" , and it feels more like a seinen. Most of the plot happens in Raito's internal monologue and conversations with the ever-present Ryuuku, and, later, in L's internal monologue and conversations with his police allies. The primarily internal nature of the narrative reminds me of Kobo Abe's work, particularly The Face of Another.
The art is very good, with a semi-realistic style that falls somewhere between Ryuichi Ikegami and Katsuhiro Otomo. Very clean linework. And ladies, Raito is definitely on the bishy side.
You can get English scanlations here. Each file is a zip containing an entire volume of the manga. The "pilot" is pretty good, but unnecessary, as it's mostly unrelated to the plot of the main series (as far as I can tell—I haven't finished the series yet); start with the first volume (chapters 1-10).