the tax revenue robbers of edoThe Shinsengumi are undoubtedly what Hijikata calls family: he has known both Okita and Kondou from a very young age and trained together at Kondou's dojo before forming the Shinsengumi. Hijikata is not only fiercely loyal to his job and to his commander, but to the group as a whole and sacrifices his very dignity a number of times throughout the series for the sake of them--everything from fighting to overcome a darker, otaku side of himself to getting on his hands and knees and barking like a dog. Next to the Yorozuya, the Shinsengumi mark a strong familial bond in the series that truly emphasize the Shounen JUMP value of friendship.
Okita SougoThere is absolutely no doubt, even for a second, that Okita would be much happier with Hijikata's head exploding in front of his bazooka: at pretty much every chance he gets he's behind Hijikata with a form of weaponry or mocking him as he dozes off on the job. While the King of the Planet of Sadists seems to spend more time finding elaborate ways to get rid of the vice commander than he does actually working, his hatred for Hijikata doesn't go completely unjustified. Many of his problems with Hijikata are rooted in their past, at a time when Okita played third wheel in both of Hijikata's relationships with the people dearest to him: Kondou and his sister Mitsuba.
Okita's tie to Hijikata remains slightly questionable, as even at the most dire of times he's been known to turn his back on him: he sides with Itou during the Shinsengumi Discord arc and only flips sides once again to save Kondou, and when he and Hijikata are handcuffed to each other in the Saw episode it's revealed at the end to be an elaborate scheme to get rid of his vice commander. Perhaps even more hideous than those two things combined, Okita dares to lace Hijikata's beloved mayonnaise with laxatives. It appears that Hijikata might be more sensitive to salvaging their relationship than Okita is: more often than not he's the one who gives into his emotions for the sake of Okita's safety (and sometimes his life). Gintama seems to leave their relationship pretty ambiguous: their relationship is always bordering somewhere between friendship and rivalry. And though any attempts to get along are normally squashed by Okita's bratty behavior, the two are inevitably fathered by Kondou and reminded of the importance of one another's company time and time again.
Kondou IsaoKondou is the beloved commander of the Shinsengumi who, despite his many many flaws (and embarassingly low ranking on the popularity poll for a main character), has a faction of men who respect him greatly and will risk their lives to protect his. Hijikata is no exception: he cares for Kondou deeply and has had a close bond with him since a young age. He's fiercely loyal to his commander and on a number of times, overcomes a great deal of trouble to protect his dignity and his position in the Shinsengumi. One of his first encounters with the Yorozuya is when Hijikata goes to get revenge on Gintoki for roughing up Kondou after he was caught creepin' on Shinpachi's sister. Hijikata is also one of the members of the Shinsengumi who stood next to Kondou's side during the Discord Arc, and even overcame his uncontrollable otaku-curse to save his life. Hijikata is a workaholic for Kondou's sake, sacrificing sleep and free time to make sure they achieve their dream and run the Shinsengumi effectively.
Though more often than not, he proves himself to be the "gorilla" that all the other characters claim him to be, the relationship is certainly not one sided. Kondou is truly the idiot with the heart of gold: he can only see the best in people, and simply wants the best for the subordinates he can only see as equals. As Hijikata is accepting (or at least, purposefully ignorant) of Kondou's unfortunate idiotic nature, Kondou is understanding to all of Hijikata's flaws as well-- including his love of mayonnaise. (Kondou grants Hijikata the day off to visit the mayonnaise factory.) What's more interesting about Kondou is the fact that in the heat of the moment, he surprises the reader with uncharacteristic seriousness and fatherly knowledge. If Hijikata is the soul of the Shinsengumi, then Kondou is the bond that holds them together.
Yamazaki SagaruYamazaki plays such an admittedly boring and plain role in Gintama (in the most hilarious of ways), but it'd be wrong to say that he's not impactful on Hijikata and the SHinsengumi in his own manner. Though every character in Gintama can be considered comic relief at one point or another, Yamazaki seems to be at the butt of every joke and at the start of every one of Hijikata's problems. When the men need new mayonnaise rules elaborated upon, Hijikata calls to Yamazaki (angrily) to explain them, even if he doesn't know anything about it. Yamazaki writes up reports for Hijikata, which normally end up as passionate essays that confuse and ultimately frustrate the vice commander. As the Shinsengumi's spy, he's often sent out to do grueling leg work for the rest of the men at Hijikata's command.
Though there are times where it's clear Yamazaki pretty much wets himself when Hijikata calls his name, there is a level of respect and devotion that comes across: Yamazaki temporarily "dies" during the Discord Arc for the sake of reporting classified information to Hijikata, as well as upholding his written rules, the Kyokuchou Hatto. He also dons the "Tosshi" outfit (and an amazing haircut) for the sake of helping Hijikata quash the inner-otaku that haunts him. Whatever the job-- Yamazaki gets it done, and whether that's out of respect or utter terror of the oni-fukuchou is completely up to the reader. At what levels he sometimes has to sink to in order to do so is a completely different story.
Itou KamotarouItou Kamotarou is the advisor of the Shinsengumi, and the spark for the discord that is started within the group during Gintama's Shinsengumi discord arc. From the beginning of his return, Hijikata is suspicious of his actions and tried his hardest to convince his commander that Itou was only bringing chaos and disorder to the Shinsengumi. However, because of Kondou's kind and accepting nature, he was unable to change his mind and Kondou was easily influenced by Itou's seemingly knowledgeable words--even going as far as referring to him as "sensei". Itou and Hijikata ultimately see each other as rivals: especially during this time, in which they were fighting to win the opinion of the commander. Itou states during this arc, in regards to Hijikata: "My greatest misfortune is that the person who understands me the most is my enemy."
However, as Itou's plan to break the Shinsengumi from within and assassinate the commander falls to pieces, he is reminded of the importance of the friends he's made within the group: the only real family and friends he'd ever had. Because of the strict rules of the Kyokucho Hatto (the disciplinary code of the Shinsengumi), Itou must ultimately die as a traitor. However, the ever-forgiving and accepting Kondou graciously grants him one last wish as a friend: to fight one last time against Hijikata, and die as both a comrade and a warrior.