In The Masks We Wear Azula informs the imprisoned Mechanist all the benefits of formally becoming a Fire Nation colony - autonomy, good relations with the Fire Nation homeland, complete support in case of dire need, the Mechanist's son getting pardoned for when he gets caught being with the Avatar, etc. - as well as the consequences of opposing the Fire Nation when Sozin's Comet finally arrives. The man quickly submits to the Princess and is implied to have accepted her offer for his people to become Fire Nation colonists.
Gerald Langer from the Mass Effect series Uplifted. He's a Nazi, literally. An anti-Semitic, homophobic Waffen SS officer who took in a young Joachim Hoch and raised him as his own son, and probably the only reason Joachim didn't end a complete sociopath. He is one of the most genuinely caring characters in the series.
Luminosity: Santiago works for the Volturi, who are...not nice people. And yet, she appears to genuinely care about everyone she works with, to the point of giving children dance lessons and needing Chelsea to cut a bond to a human so she doesn't mourn too much.
The My Little Pony/Sonic the HedgehogCrossoverChaotic Harmony: Sonic is a huge Jerkass thanks to no action over the course of a year. He completely ruined Cream's birthday party, split all ties with his friends, and thought about deserting his friends in Ponyville after they were transported via Chaos Control. But even after all of that, he couldn't resist helping Rarity finding her missing goggles that she needed to finish her design. (That Sonic helped model, no less.)
In the A Song of Ice and Fire fanfic, Times Like These, gives a surprising one to Aerys of all people. Apparently, Aerys had a portrait of Steffon Baratheon, Robert's Father, as a babe placed in the Throne Room, because Steffon was loyal and, considering Aerys' state of mind, states that he misses him! Stannis was surprised to see the portrait in such a public place to say the least when shown.
Christine Hargensen might have been a mean Alpha Bitch who enjoys tormenting her classmates, but in the Carrie fanfic "BF Fs?" she appears to be a caring friend - even going so far as to cuddle one of her clique when she has a nightmare.
A series of Casper fics, theWhipstaffTales, are basically one big series of pet the dog moments for The Ghostly Trio. Stretch in particular, who ends up in a rather sweet uncle/niece relationship with Kat's daughter, Amy.
The Rise of the Guardians story, Lullabies, has a moment for Pitch. While he only gave the Guardians parenting advice because his daughter asked him to, he really didn't have any personal gain in saving Jamie and Jack from drowning.
Safe and Sound, a Star Trek fic, has Khan adopting Lucille Harewood after she loses her mother. While he considered her as a replacement for the child he lost, it's still rather sweet considering who this guy is.
Even Wily gets one in a twisted way when he attacks an hallucination of his father after it threatens ProtoMan.
Wily invokes and weaponizes this in Episode 11, using a hug with Bass to hurt ProtoMan.
In A Black Heart before he heads to Soul SocietyIchigo, who's an unrepentant mass-murderer, calls up his accountant and tells them that unless he gives them explicit instructions within the next two weeks to transfer everything he owns to his adoptive sister Tatsuki.