This article contains major SPOILERS. Be careful if you do not know the full story yet.
The fate of Hakuouki characters is a big spoiler and can differ depending on whether it is an anime, a movie, a game, a live action, or a spin-off (or even a spin-off live action for that matter). Hence why everything depends on the exact version of the story.
Common theme
Hakuouki is set in a specific timeline and a sequence of historical events that the Shinsengumi are part of. These events happen regardless of the character choices and serve as a backbone of the story as they remain the same. However, singular character's participance may change depending on the storyline and adaptation.
Chizuru survives the events in most of the cases, there are only a few occurrences where she is murdered.
Hijikata Toshizou
Despite being a titular character, Hijikata dies in most of the storylines. He survives in his own route in Shinsengumi Kitan and Edo Blossoms, however, all the other routes show or mention his death. The anime series also implies his demise but leaves the finale open to debate. The second movie, however, shows explicitly that Hijikata survives and continues his life with Chizuru. His game route has only one positive ending for Hijikata to survive, 2 of them imply his death and 4 imply Chizuru's death which is why Hijikata's future is unclear.
In Sweet School Life, Hijikata is re-imagined as the Vice Principal of Hakuou Academy in 2015, who teaches Classic Literature and is also a Disciplinarian Adviser, his life is not tragic anymore, and he is still a potential love interest for Chizuru.
Okita Souji
Okita does not always appear in the games after a certain point, because as Chizuru chooses her love interest this person becomes the focus of the story, shadowing others. If Chizuru does not pick Okita, his appearances are scarce and he is either known to be dead or never mentioned again, or may appear for a short moment (like on Hijikata's route) only to then be announced dead later in the plot. However, if Chizuru does choose Okita, she can stay by his side helping him through his illness and later even share his pain as a Rasetsu since Okita's route is the only one where the main character is forced to drink Ochimizu. Reaching the good ending, they find a way to cure them both and live as long as they can. In tragic endings Okita either kills Chizuru himself after he loses control during a fight with Kaoru, or he tries to protect her and dies in her arms.
In the anime series and movies Okita dies approximately at the same time after Kondou's execution due to using up all his lifespan fighting Rasetsu. In Sweet School Life he is re-imagined as a second-year student at Hakuou Academy in 2015, who is part of the kendo club and is keen on taking photos of everything and everyone he finds amusing.
Saitou Hajime
Same as Okita and others, Saitou stops appearing in the games after a certain point if his route is not chosen. If he is mentioned in any way, Saitou always dies during the Battle of Aizu, whether it is the anime series, the movies or the games. In the movies and his game route he drinks Ochimizu and becomes a Rasetsu. His route, however, has a happy ending where Saitou survives and stays with Chizuru.
In Sweet School Life he is re-imagined as a second-year student at Hakuou Academy in 2015 and a member of the Discipline Committee who takes his job very seriously. Apart from studying, Saitou practices in the kendo club.
Harada Sanosuke
Harada is the only character who never becomes a Rasetsu in any of the adaptations. In both the anime and the movies he separates from the Shinsengumi and pursues his own agenda, but eventually dies fighting alongside Shiranui, and in the games his fate in the same in most routes except for his own. In Harada's route Chizuru gets a happy ending as Harada stays alive, they get married and have a child.
In Sweet School Life, Harada is re-imagined as a PE teacher at Hakuou Academy and his life is far from tragic as it is filled with looking after students and Shinpachi who often borrows his friend's money.
Nagakura Shinpachi
Shinpachi's fate is the most positive in all the adaptations as he is never seen dying (he is mentioned as one of the dead in the anime series but his demise is never shown). In the games his fate is quite vague as he stops appearing quite quickly (outside of his own route), so even his demise is not always certain. He separates from the Shinsengumi along with Harada, and on his own route he is forced to become a Rasetsu and suffers from bloodlust. His route was not part of the original game but was added to Edo Blossoms.
In Sweet School Life, Shinpachi is re-imagined as a math teacher at Hakuou Academy living with Harada. He loves horse racing and drinking and wastes his money thoughtlessly.
Toudou Heisuke
Heisuke is the first one to become a Rasetsu after Sannan, this fate never changes in any outcome. He hates himself for it in the movies and in the games, and Chizuru helps him through it. In all the routes except his own he either dies behind the scenes and is only mentioned as one of the deceased ones, or his demise is shown, and is similar to the anime series where he fights multiple Rasetsu and uses up all his life force. In Heisuke's route there is a possibility of a happy ending despite a dark storyline with Koudou and Sannan as true antagonists.
In Sweet School Life, Heisuke is Chizuru's childhood friend and a student at Hakuou Academy. He has a gaming addiction and he is part of the kendo club alongside Saitou and Okita.
Sannan Keisuke
Sannan is always the one to research Ochimizu and quickly turn into a Rasetsu. Both in the anime series/movies and in the games Sannan eventually joins Koudou pretending to be on his side but in truth spying on him for the Shinsengumi. However, in Heisuke's game route Sannan becomes an antagonist actually believing that Koudou's plan should come true. In his own route Sannan survives but in all the other routes he either dies like in the anime series and movies by using up his lifespan at the time his true allegiance is revealed, or his fate is not mentioned (but his death is still implied as only a few Shinsengumi stay alive at the end making all the other ones automatically dead).
In Sweet School Life, Sannan is a doctor at Hakuou Academy.
Kazama Chikage
Kazama was initially created as a very simple "always bad because bad" antagonist who appeared in all the routes and fought against the Shinsengumi. In Hijikata's route, the vice commander is his nemesis as well as in the anime series and movies. In Okita's route, Kazama last appears after Chizuru has turned into a Rasetsu which the demon sees as an abomination and abandons his attempts to make her his wife. In the anime series, Kazama sees his plan through and dies fighting Hijikata, while in the movies he is only slightly wounded and agrees to leave after the fight.
Kazama's route in the games is very different to all the other routes as his storyline is not related to the Shinsengumi but to Chizuru's search for her father and brother in order to stop their plan to create a demon kingdom. Kazama is the one to save Chizuru after Inoue's death and then he stays by her side and supports her, and they eventually live together for over a year chasing after the Shinsengumi commanders that Chizuru wants to meet for the last time. Finally getting to the last battlefield and learning about the Shinsengumi's fate, Chizuru decides to stay and Kazama leaves to help his clan but kisses Chizuru and promises to come back for her. In the final scene after the game credits he does come to Chizuru to marry her, they share a kiss and stay together. This route was partially used in the anime and movie adaptation to add Kazama's character more depth and show other sides of his personality.
In Sweet School Life, Kazama is re-imagined as a third-year student at Hakuou Academy who is much older than other students and ends up being the President of the Students' Council.