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.
In stark contrast to the original, Shinji, Rei, and Asuka in Shinji And Warhammer 40 K 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.
Mortality has a veritable clan of True Companions, people who are drawn to Sherlock Holmes for friendship and for his own protection. Brother Mycroft, landlady Mrs. Hudson, Dr. Watson (naturally), his wife Mary, Wiggins of the Baker Street Irregulars, Inspector Lestrade and his own family... And this is only the core of the group - there are many more unnamed Irregulars and Yarders who would do anything for the Great Detective.
The Lucky Star fanfics Holiday Vacation and Lucky Star After Story portrays Mariko Aratani and Chiyoko Sakamoto, two of the original characters, as this. They've actually been best friends since the day they started kindergarten back in April of 1996.
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.