This is one that I started reading recently. A friend's brother collects them and it was recently made into a movie. Death Note written by Tsugumi Ohba and illustrated by Takeshi Obata.
Light Yagami is a high school student who discovers a notebook, known as the "Death Note". The Death Note says that, if a name is written in it, the person will die. Light is skeptical of the Death Note's authenticity, but after experimenting with it and killing two criminals, he is forced to admit the Death Note is real. After meeting the true owner of the Death Note, a shinigami (Death God) named Ryuk, Light seeks to become the "God of new world" by passing judgment on criminals.
Soon, the number of inexplicable deaths of reported criminals catches the attention of the International Police Organisation and a detective known only as "L". L learns that the serial killer, dubbed by the public as "Kira"(derived from the Japanese pronouncation of the English word "Killer" and also from the Latin word for "light"), is in Japan. L also concludes that Kira can kill people just by knowing their name. Light realises that L will be his greatest nemesis, and a race between the two begins.
Death Note has been made into a movie that is mostly faithful to the manga (with some slight alterations such as the addition of Light's girlfriend Shiori).