Light Yagami, the teenaged protagonist, is the only person who can see the demon who gave him the Note, and he and the demon trade quips as Light sets out to improve the world by killing all of its worst criminals. This works for a hundred or so deaths, but then the G8 and Interpol sic L, the world's greatest, most mysterious sleuth, on the trail of "Kila" (killer), the person responsible for all of the killings.
The pacing is very tight, with surprising twists and turns. Light is a great, cheerfully amoral killer, a teenaged megalomaniac who delights in using his prodigious smarts to test the limits of the Death Note, approaching it like a Royal Society natural philosopher devising a series of tests to determine its parameters, to the delight of his demon companion.
The total absence of any disapprobation for Light's deeds is what sets this apart from American vigilante comics. In those books, there's always someone there to wag a finger at the crimefighter, even if it's just the crimefighter's own tortured conscience. That might appear in later volumes of the Deathnote books (I've only just read the first collection, there are 11 in print or due soon).
I don't read a lot of Japanese comics, but this came highly recommended by Secret Headquarters, my local neighborhood funnybook emporium, whose proprietor, Dave, has yet to give me a bum steer. It's a real treat living near a great comics shop.
Update: Dan sez, "it is also is about to be a major Japanese movie, being released later this month throughout Asia."
Update 2: James sez, "Two Death Note films have been released in Japanese theaters. The latest one, 'Death Note: The Last Name,' was a huge box office success when it was released a couple months ago."
Update 3: Hung sez, "there's also an anime series running right now in Japan. It started running around October of last year."