A Crown Of Stars: The Avaloni troops left stranded on Earth quickly became this: Shinji, Asuka, Hikari, Touji, Kensuke, Misato, Kaji, Ching, Bir, TJ… develop this kind of comradeship throughout the war campaign.
Advice And Trust: Hoping getting her sync rates up, Gendo commands Rei spending more time with Shinji and Asuka. As a result of it, their bonds strengthened and they became true friends and siblings-in-arms. Hurt one of them and the remainder two will ensure that you REGRET it. Bardiel and Zeruel learnt this the hard way.
Doing It Right This Time: After surviving the Angel War, dying before being fifteen, outliving the end of the world and going back to the past Shinji, Asuka and Rei are trying to save their future. As a result of this they are bonding and their relationship becoming stronger.
We may hate things about each other, but in combat we know we can trust each other with our lives.
In a very odd way, Alpha Brass and Twilight Sparkle from This Platinum Crown. He is legitimately incapable of feeling any emotions because he was so royally screwed up by Chrysalis, but during the Equestria's Strongest Couple duel it's shown that he does seem to care for her, if in a less romantic way than normal for this trope.
The pack in the ''Canisp'' series. None of them are related (except for a pair of sisters), but Meya and Canisp consistently refer to each other as "sisters". When one of the group makes a mistake that nearly kills them all and lands one of them with a broken leg and a concussion, they all stand up for him against the rest of the Wolves, insisting that it was an honest mistake and he learned from it—this in spite of the fact that one of the group spends most of her time glaring at him.
The Chance Encounter crew. Strange, dysfunctional and prone to good natured bickering, they have gone through hell for one of their friends.
Shinji And Warhammer 40 K: Shinji, Rei, and Asuka in are definitely this trope. They may have others that are close to them, they may view every human as someone to protect, but their role as Pilots has created a bond that no-one else shares. Mana even expresses frustration at how improbable it is that she will ever be a part of it, but is content that her role results in her being closer to them than anyone else.
The Malificent 11 from the Daria series God Save The Esteem will beat each other on an hourly basis, but Heaven help you if you look at (or near) any of them even slightly askew.
Also from DariaFan Fic, The Alliance (a cadre of military cadets from the long-running ficLegion of Lawndale Heroes) was intentionally created to be this, in keeping with the academy's efforts to provide familial connections for the cadets.
The Pony POV Series naturally has the Mane Cast (which grows to include Trixie and Fluttercruel), but also has the Cutie Mark Crusaders (which ends up including Spike and Silver Spoon) and Misfit Actual (Shining Armor's squad).
While NCIS pretty much covers this already in canon, the Doorstopper fanfic "Shards To a Whole" takes the trope Up to Eleven. While the emphasis remains on the developing relationship and marriage between Tim and Abby, much of the fic centers around how the team bonds into a true family. At one point, Abby designs a Team Gibbs Coat of Arms, while in more recent chapters Ducky and his new wife Penny (Tim's grandmother) sell the newly-retired Gibbs on their idea of purchasing a run-down estate to serve as a second home for the whole NCIS team, once the team get together to restore the mansion.
Rosario Vampire: Brightest Darkness: Even after they find their own boyfriends and move on from him, the various members of Tsukune's Unwanted Harem, as well as said boyfriends, remain close friends with Tsukune to the extent that, in Act III chapter 52, he openly states that he would gladly die for them and can't imagine living without them.
Nightblade: The main cast develop into this. Nick especially relies on this because these are the only people in the world he trusts and cares about.
As in canon, we have Zoro, Nami, Usopp, Sanji, Chopper, and Robin thus far, but in an effort to avoid having his crew overpowered by Marines again in the future, Luffy has actively tried to make his crew bigger this time.
Gin is the first new addition, after Luffy thrashes Krieg…and giving implications beforehand that his captain wasn’t all he claimed to be. Gin realizes this after he loses to Sanji, and at the end, when his resolve to return to the Grand Line is finalized, Luffy extends the invitation. He accepts.
Nojiko also decides to come along to see Nami see her dream through. Well, that and to make sure she’s safe after catching Luffy and Nami in a Lemon.
Yosaku and Johnny are given an invitation when the crew is en route to Arlong Park. They accept in the end.
Crosses over with Enemy Mine above; after a couple of brutally effective Curb-Stomp Battles, as well as learning that Baroque Works’ true intentions do not aspire towards an ideal nation, three of the officer agents join the crew: Miss Valentine in Whiskey Peak and Mr. 5 and Miss Goldenweek in Little Garden. At the end of the Alabasta arc, Mr. 5 reluctantly leaves the crew to seek his own dreams, but the other two become permanent members.
Vivi also elects to remain with the crew after hearing about Luffy’s past and the World Government’s atrocities towards everywhere that he had visited, understanding that her country is still in danger and she can’t do anything about it by staying behind.
Children of an Elder God: In spite of all their fights and arguments, Shinji, Asuka, Rei, Touji and Hikari are a team and fight together during the War. After the Final Battle they think of themselves as a family.