The story revolves around a juvenile delinquent, Yuusuke Urameshi, who, in the first minutes of the anime, DIES saving a child from a traffic accident. Wandering around as a spirit, confused as hell, he meets Botan, a ferry-girl who guides spirits to the Reikai (spirit realm) after death. She informs him that his death was totally unpredicted and unexpected, a mistake, so is given a second chance at life by Enma Daiou (Lord of the Dead), by undergoing a series of challenges and tasks, thus becoming a Reikai Tantei (Spirit Detective). One of Yuusuke's first tasks is to recover 3 treasures stolen from the Reikai. Two of the thieves, Kurama and Hiei, are later 'punished' by having to also to do services for the Reikai and become spirit detectives, but of course later they become best friends.
Yuusuke's attack is a Rei-gun (spirit gun), a bolt of energy shot out from one finger with his hand shaped like a gun, capable of great destruction. He also uses his fists a lot in a fight, being more physical than, say, Kurama. He mightn't seem too bright, but often surprises even the most experienced opponents with his actions. He can be arrogant, but brave, determined, he adopts a happy-go-lucky, reckless attitude that often gets him into strife but comes out stronger for it at the end. He thrives against stronger opponents, being able to increase his power tenfold in a short period of time with hard training. In the end it's always his childhood sweetheart, Keiko Yukimura, who's his inspiration.
Kurama is a youko (fox demon) reincarnated as a human, the (now) teenaged 'Minamino Shuuichi' (his human name) is a top-student and perfect son. He uses his youki (demonic energy ?) to manipulate plants, his preferred weapon is the Rose Whip, which can slice, dice, and chop away his opponents. In times of extreme danger, when angered, or in other special circumstances he can revert to his youko form, thus becoming MUCH more powerful. He's good-natured, kind, polite and best friends with Hiei - he's the only one who can make fun of him and get away with it. ^.^
Hiei is a fire demon with a Jagan ('evil' third eye) giving him the ability to use the 'black fires of the Makai' (demon realm) in attacks like the Jaou Ensatsu Kokuryuuha (a huge firey black dragon, which normally stays as a purple tattoo winding around his arm, which can easily annihlate enemies). Hiei has a dark past, abandoned as a child, he was raised by a band of thieves. He has no qualms about killing anyone, and went to the Ningenkai (human realm) to search for his long-lost twin sister. Hiei's really short, with a grumpy demeanor, he has a trademark scowl and often answers a short, distainful 'Hn' when questioned. He can be arrogant and is always eager to fight. Hiei and Kuwabara can't seem to stand each other, constantly bickering and at each other's neck, but deep down they're friends.
His longtime arch-rival Kuwabara Kazuma (who constantly tries to best Yuusuke at fighting, and constantly gets a royal whipping) later becomes his best friend, joining him as a Spirit Detective. Kuwabara shapes his reiki (spirit energy) into a weapon, the 'rei ken' (spirit sword). Kuwabara may seem loud, annoying, and not as 'attractive' as the other three, but he definately can't be underestimated. Like Yuusuke, he was a juvenile delinquient at school, having an arrogant and tough-guy macho attitude, but inside he's a big softie, caring and unconditionally loyal to his friends, possessing a huge inner-strength, in the end he also proves he's as smart as anyone else, maybe even smarter, when he studies hard to get into university.
The four have many adventures together, like competing in the Ankoku Bujuutsukai, a (martial arts?) tournament, facing foes like Toguro, later Sensui. Though some may say the animation isn't exactly exceptional, its plot sets it apart from the rest. The characters are highly developed, the heros have flaws and develop, and the villians aren't always the clear-cut baddies who are totally evil, but they have their own agendas, which often don't turn out to be 'evil' at all. Actually, the whole defintion of 'evil' and 'demons' are turned inside out and upside down, as two of our heroes are demons themselves. The theme of friendship, comradeship and even love is prevalent, Yuusuke overcomes seemingly impossible obstacles, changing and growing from a young, undisciplined drop-out to a truly admirable hero who never lets down his friends, and becomes immensely powerful. Among it are many interesting sub-plots about the other characters, there being a large number of 'minor' characters, offering refreshing scenes every episode.
I personally feel the second movie 'Poltergeist Report' didn't do the anime or manga series justice, as the plot was a bit serious and lacked the comedy in the original series. By all means, do watch it, but people who haven't seen the anime may not understand why Yuusuke has these powers, or why Hiei and Kurama are fighting on Yuusuke's side if they're demons. I don't think I enjoyed the movie that much because the villain, Yakumo, was totally devoid of the separate agenda and 'human side' that YYH showed as a series, like the excellent opponent for Yuusuke, Sensui, with his multiple personalities and reasons behind his (albeit deranged and destructive) actions. Hinageshi was totally unnecessary, I feel, Botan was portrayed as too serious, Keiko too much of a damsel in distress, Genkai too harmless... but after all that criticism, I think that all YYH fans should see this movie, and non-fans should see it because it's the only easily obtainable English form of YYH, and also it may help you decide whether you want to search for more YYH.
I HIGHLY recommend YYH, go see it! ^_^