This is the story of a 14-year-old juvenile delinquent who dies once, but is brought back to life to work as a sort of psychic detective/troubleshooter. As his "Ki" powers increase, he and his friends (who include 2 demons) run into more and more nasty-bads. Finally, they are challenged to a gigantic demonic competition, which unfortunately lasts a grand total of 7 books out of the entire series, though it supposedly lasts only about 10 days. They win, of course, but are immediately faced with the problem of Some (Powerful) Idiot opening a hole between the Real World and the Demonic Plane. After that, things rapidly wrap up.
Book 1: Our Hero (Yuusuke Urameshi), dies while trying to save a child from being struck by a car. This is so amazingly out of character for the fight-prone, violent, stupid guy, that the Spirit World wasn't prepared for his death. So, Yuusuke and his Spirit Guide (actually, a minor goddess of death) named Botan (Button) wander around in spirit form as the Spirit World tries to figure out what to do with him. Yuusuke watches various human stories unfold, and does Good Deeds.
Book 2. Same as above. He finally returns to life at the end of this book, when his childhood (girl)friend helps revive him.
Book 3 - 4. Yuusuke must defeat 3 demons, who have stolen powerful Spirit World artifacts. One he kills, one he helps, and one he defeats. The latter two, Kurama and Hiei, later turn into his friends (in fact, at one point later on, a popularity poll showed that Hiei was more popular than Our Hero. In the TV series, Kurama was the most popular). Later, Yuusuke and his "eternal rival," an ex-gang leader named Kuwabara, try out for the position of apprentice to a master of Rei-Ki. The master of Rei-Ki is an old, short woman by the name of Genkai. Think Yoda. He calls her "hag," and she insults his intelligence. They make a great master/apprentice team.
Book 4 - 5. Yuusuke, Kuwabara, Kurama, and Hiei are sent off to stop several Demon World villains, who have gained control of evil demonic bugs that make people go crazy. The 4 discover that together, they are a formidable team (even if sometimes they can't stand each other). This is the beginning of their deep friendship (though Hiei would deny it). In the meantime, Yuusuke's girlfriend and Botan must defend themselves against an onslaught of people who are mind-controlled by these bugs.
Book 6. Yuusuke and Kuwabara are sent to rescue a demon-girl (Yukina) from the clutches of a rich, nasty man, who has imprisoned her for her magical gem-tears. Kuwabara instantly falls in love with her. Yuusuke doesn't tell him that the girl is actually Hiei's younger half-sister. Later in the book, Yuusuke, Kuwabara, Hiei, and Kurama are all forcibly invited to the Demonic Competition. The reward: anything they desire. The price for failure: death.
Book 6 - 13. The competition. Our hero's team is composed of Yuusuke, Kuwabara (who loses a lot), Hiei, Kurama, and Genkai (the "hag" mentor). Battle after battle after near-death experience after battle.... Cool battles, mind you, with the heroes having to use their brains as much as their technical skills.
Book 13 - 1?. The Demon-Real World hole becomes a problem.... Yuusuke and friends must fight to contain a hole that is forming between the Demon World and the Real World, eventually resulting in a major battle between the madman who started the whole thing, and Yuusuke. Yuusuke dies once more, but comes back to life ... because a demon lord was one of his ancestors. Thus Yuusuke is reborn as a demon (sound a little bogus yet?) and finally wins, only to find out that the madman who started the mess had done so because he wanted to be killed by a powerful opponent. Weird, huh?
Book 1? - ?. Yuusuke goes off to meet his ancestor demon. Kurama and Hiei are recruited by 2 different rival demons. Kuwabara surprisingly begins to study hard for high school exams (!). There is trouble in the demon-world, and power struggle; to solve it all, Yuusuke, who has inherited a kingdom in the demon-world from his demon lord ancestor, goes off to each of the other powerful lords and proposes a giant contest to see who'll get the rule. Just for fun. Just for the heck of it. Everyone agrees, and another contest begins.
Book 17 (?). Yuusuke eventually loses the contest, and comes back to the real world. In the meantime, the demon-world starts communicating with the human world, and some of the contestants from the first competition start becoming TV personalities. Really. Hiei stays in the demon-world with his lord/master (a young woman with a dark past). Kurama stays in the human world, learning about his new step-father's business. Yuusuke opens a food stand. Kuwabara keeps studying. The last adventure occurs when terrorists take over the Spirit World, threatening to kill a lot of innocent people (spirits?). Yuusuke and his friends are sent, one last time, to defuse the situation. (Literally defuse, since the terrorists have left a powerful time bomb behind). Yu Yu Hakusho ends on a surprise note (a whimper, not a bang); apparently the author had been feeling pressured by Shonen Jump to do things with the plot that he didn't want to. Too bad, but one could feel that the manga was beginning to lose toward the end.