Call of Juarez: Bound in Blood is ALL about this trope (hint: the title is a clue). The whole story is basically about the three McCall brothers dealing with their differences in all the wrong ways until the very end. In fact, the tagline of the game could be "We are a family".
The loyalty missions in Mass Effect 2 are supposed to resolve the deepest internal conflicts and motivations of their respective characters. Not surprisingly, half of them revolves around family matters: Grunt finds a tribe for himself; Jacob deals with his Disappeared Dad; Miranda rescues her twin sister; Samara tracks down her daughter; Tali has to deal with the blowback of her father's covert misdeeds; and Thane tries to return to his paternal duties.
Then there's Legion, who may not necessarily have blood, but in a weird way his loyalty mission does involve his family.
And it was hardly the first time BioWare played that card. The "messenger" quests in Knights of the Old Republic serve much the same function. Carth's Dark Jedi son, Bastila's mother, Mission's deadbeat brother, the utter clusterfuck on Kashyyyk regarding Zaalbar's family...And while it probably isn't blood related, the Mandalorian concept of "family" would put the Jagi and Canderous on this, too.
The original Dragon Age: Origins has a sidequest which subverts this. Alistair knows he has a half-sister and he's always wanted to visit her, but when he does, she wants nothing to do with him and denounces him for trying to intrude on her life without giving her financial support.
Especially nastily averted with Morrigan and Flemeth. Blood ties are fine and dandy but they're not going to dissuade Flemeth from stealing Morrigan's body or Morrigan from having Flemeth killed. (It's not clear even to Morrigan whether Flemeth is Morrigan's biological or adoptive mother, but Morrigan considers this detail irrelevant.)
The City Elf Origin has got an example, with slight variations depending on the Warden's gender. In either case it consists of an elf and the Warden's cousin breaking into the Arl of Denerim's estate to rescue the kidnapped female wedding guests, and then the Warden teaming up with the aforementioned cousin to rescue a third cousin from the heart of the estate.
Dragon Age II plays this trope straight sometimes. You can be a complete ass to Carver, drive him to join the Templars, and at the end he will still step between Meredith and Hawke and say "I will not kill my own brother/sister".
It is, however, averted in the case of Bartrand and Varric, as well as with Merrill and her clan.
Gamlen comes close to referencing this trope by name while averting it, actually. He does however play it straight with his desperation if he is picked to help find Leana after the Serial Killer gets her and more cheerfully, if you opt to reunite him with his long-lost daughter.
It's also possible to avert it by joining the Templars and killing Circle!Bethany.
Archibald Ironfist is not a good man (for starters, his scheme to get the crown involves arranging for the murder of the Royal Seer, and then continuing to murder the successors until he can put the blame on his brother Roland). He also clearly feels a familial connection to Roland (note that he could just have arranged for his brother's murder to get the throne, but doesn't; and even if you side with Archibald and defeat Roland, he still merely locks Roland up rather than execute him), culminating in Archibald risking his neck to save Roland from a horrible fate in Might and Magic VII.
In Shellshock 2, Nate's main motive throughout the game is not the orders he has been given or even a desire to stop The Virus. He just wants to find and help his brother Cal. In the end, he has to choose between a) saving Cal; and b) saving the villain so as to make him provide a cure. It's up to the player, but if players do choose to stick to this trope, the epilogue tells them that Cal dies a few weeks after his rescue anyway, while the zombie plague rages on.
In Lost Horizon, Lord Weston, governor of Hong Kong, takes this approach towards his missing son. He initially pretends otherwise, making a show out of downplaying his personal investment in the disappearance — he says he can't let the identity of the missing officer affect his duties. In reality, though, he has been secretly cooperating with the Nazis as a backup plan in case Fenton can't (or won't) rescue Richard. He eventually betrays Fenton to the Nazis for this reason.
At the end of Devil May Cry3, the twin sons of Sparda Dante and Vergil have just fought a vicious duel over the artifacts containing Sparda's power (Vergil wants to use that power to take over the world and Dante wants to stop him), a duel that Vergil loses. The defeated Vergil has barely enough strength to reclaim his half of their mother's amulet and warn his brother to leave before the portal between the human world and Demon world closes. He then allows himself to fall over a cliff. Despite everything that has just happened, Dante instinctively reaches out for Vergil's hand to save him. Vergil slashes his brother's hand in response since he wants to stay in the Demon world. It may also have been the only way Vergil knew how to show concern for Dante.
Fire Emblem Fates: The Nohr Siblings Xander, Camilla, Leo and Elise knew that their father Garon lately has been acting really evil and not exactly being a man to be cheered at. Even so, they still stuck with him as he's still their father and they swore not to betray their families after the Deadly Decadent Court that they have faced since childhood that costed the majority of their other siblings. When Garon is revealed to be a slime monster impersonating their father, all bets are off and they're more than glad to rip the impostor a new one, finally accepting that the real Garon has been dead for a long time.
Overwatch: Hanzo is a honorable person overall, but his honor lies within his family loyalty. Therefore, he was being The Dutiful Son to his criminal empire family, never minding their unsavory business because it's still his family, and wishing that his brother Genji would feel the same. Unfortunately, his brother has a different idea about valuing honor, it should be on actions. When Hanzo ended up obeying the order that would look like it killed Genji, he was so distraught that he spilled the blood of his family member, he left the clan in shame. But when Genji came Back from the Dead and was actively shutting down his family business and being a Cyber Ninja, Hanzo viewed it as a violation of honor and ended up acting bitter against him.
A racial version in the Apocalypse launch trailers for Stellaris. The Commonwealth of Man has strong ideological disputes with the United Nations of Earth, but at the end of the day, the two powers are still human. When the UNE colony of Europa VII is destroyed by an alien superweapon, this gets the Commonwealth to mobilize and counterattack against the Gamma Aliens with their own apocalyptic weapon to protect their fellow humans.
Uncharted 4: A Thief's End features this in the relationship between Nate and Sam. Sam forgive Nate leaving him in jail given the circumstances of the botched escape. More dramatically, Nate, Sully and Elena, whilst obviously upset, are completely forgiving of Sam having made up a motivation to get Nate into an adventure again and risking his life many times over the course of the game, and at one point Nate's marriage to Elena as well.