When an anime is centered on a character who dies in the first episode, as is the case with Yu Yu Hakusho, death becomes a complex issue within the confines of the story. For some shows, death is a dramatic concept, while for others, it's more a mild inconvenience. When a character dies in Death Note, that's it for them. In a series like Dragon Ball Z, it is expected that dead characters will return to life within the saga.
However, Yu Yu Hakusho has a very complex relationship with the dead throughout. While the main character, Yusuke, dies twice in the series, death still manages to be this concrete consequence of life that some characters fight to avoid while other characters greet almost too eagerly. So how is death handled in the world of Yu Yu Hakusho?
Death as Another Stage of Life
Death throughout Yu Yu Hakusho is presented as just another stage of life, one where those who die aren't truly gone but instead placed in a state of transition. This is clearer in the first arc of the anime and manga, where Yusuke dies and returns to life. He has minimal interaction with the world around him as he tries to return to his body. He then later dies a second time during the fight with Sensui, only to, once again, return to life. Genkai is killed by the Younger Toguro brother, only to return to life again. There are other examples of this, such as when Tsukihito Amanuma, one of the Sensui Seven, is killed and returns after confronting Kurama in a death game of his design. Death is not the end for these characters.
The afterlife, likewise, is its own government with its own bureaucracy and order. We see Koenma, the son of King Enma, dealing with paperwork from the Spirit World. Yusuke causes issues because his death defies the expectations of the typical procedure. Once again, death is another stage of life, complete with the power structures that make living society both complicated and frustrating. It also doesn't help how decisions in the afterlife political body, such as King Enma's manga-only attempts at painting Demon World as a genuinely awful place, directly impact human society.
There is a manga-only storyline that was never adapted centered around Matsuo Suekichi. This story takes place during Yusuke's time as a ghost, where we see Yusuke help Matsuo become a boxer via helpful possession. In this case, the dead directly help the living, indicating that death is never the end in a straightforward way. The anime foregoes this plot, and in doing so, loses one pivotal moment where Yusuke interacts with the world beyond as a spirit. This link between life and death is foregone in favor of getting to Yusuke as Spirit Detective faster.
Far Worse Things than Death
Of course, all things can die in Yu Yu Hakusho, but some fates are worse than death. Like Yusuke and even Genkai, humans can die and return, as seen by Genkai's rebirth following the Dark Tournament. However, death can also affect demons as well, as seen with Younger Toguro's quest to seek death at the hands of someone stronger than himself. This is his true motivation which leads him to create an adversary in Yusuke.
Toguro sees death as the only punishment he's worthy of receiving. While many demons die in the series, the Toguro Brothers face very different fates, which reflect on their deserved punishments for their sins. The Younger Toguro, who has come to terms with his sins, welcomes death. Arguably, he welcomes his attrition in death too much, accepting a punishment far worse than the one he deserves by Koenma's accounts. At the end of his cycles of rebirth in Hell, Toguro will face total obliteration of his essence. However, Elder Toguro, who is far more malignant, ends up suffering an eternal nightmare thanks to Kurama.
Death is not seen as the worst fate that can befall a person. The destruction of a soul is a far more genuine horror, as seen early on during the Artifacts of Darkness arc. However, while Yusuke has a serious problem with Goki stealing souls directly from children, he has less of a problem with demons in the Three Kings Arcs admitting they eat human flesh. To Yusuke, eating a soul is cruel because they cannot pass into the afterlife, but eating flesh is just a means of survival. Once again, death is not nearly as final as total obliteration or an unending nightmare. Death, after all, isn't all that bad -- in Yu Yu Hakusho.