Piccolo of Dragonball Z becomes one to Son Gohan, the eldest son of his one-time enemy Son Goku. He appears to be willing to be this to any non-pure Saiyan in the series afterwards: this inclues Gohan's brother Goten and Vegeta's son Trunks (the one not from the future) in later Z episodes, plus Gohan's own daughter Pan in Super.
In Fruits Basket, martial artist Kazuma Sohma takes his distant nephew Kyo in and serves as his father figure. Eventually, he also takes his distant niece Rin in.
And before that, Rin was "rescued" from her Abusive Parents by her cousin Kagura's parents. The rescue of sorts was genuine, but poor Rin was already so messed up by her abusive situation that she simply couldn't accept or fit in with a more stable family, and distanced herself from them despite not having ill will towards them.
Dr. Juuzo Kabuto raised his grandsons after their parents died in a lab experiment gone wrong. After his death, Sayaka's father/Juuzo's former assistant Prof. Yumi took Kouji and Shiro in. However, in practice Kouji was Shiro's main parental substitute from before this took place (although somewhat absent, since Kouji had to split his time between taking care of the household chores, going to school and fighting Mechanical Beasts).
After the end of the Mazinger series, Kouji and Sayaka left Japan for a while, and Shiro was left behind in the beginning of Great Mazinger. He was taken in by Professor Kenzo, which is ironic, since he his -and Kouji- REAL father, but he doesn't tell the boys about it for a long time.
In UFO Robo Grendizer, Dr. Umon found and took a young and traumatized Duke Fleed in, renaming him Daisuke and treating him like his son.
In Basilisk, male lead Gennosuke Koga is raised and trained by both his grandfather Danjou and his maternal uncle Hyouma Muroga, who was just out of his teens when he took up the role. His girlfriend Oboro, on the other hand, is raised by a nanny (who later dies) and her grandmother Ogen. Also, Oboro's fellow Iga ninja Koushirou was pretty much raised by his Evil Mentor, Tenzen.
In Naruto, Iruka Umino couldn't forgive Naruto for a long time since he was the living seal for the Kyuubi, which killed his parents. As years passed, though, Iruka slowly came to appreciate Naruto for the person he was, realized that aside of the Kyuubi issue they were Not So Different, and by the time the series starts he acts like a surrogate father to him. To the point that when the grown Naruto marries Hinata, he explicitly asks Iruka to come to the wedding as his father.
Kurenai Yuuhi acts as a surrogate mother to Hinata, after Hinata's strict father all but abandons her for a long time.
It is strongly believed that Tsunade took her apprentice and Sexy Secretary Shizune in as a sort of surrogate daughter. This isn't without basis: Tsunade's fiance Dan, who also happened to be Shizune's uncle and, as far as one knows, her only living relative, was killed in battle.
In Axis Powers Hetalia, China raises some of the East Asian nations, but they see him more as a brother than a father. In fact, Korea refers to China as "Aniki" ("Bro"), a rather informal term for "older brother": this is pretty important since the others don't fully acknowledge China as a brother - Japan and Macau call him "Mr. China" while Taiwan and Hong Kong refer to him as "teacher".
Same with England and young America. Despite what bash-happy might tell you, they also have an older brother/younger brother relationship, with America at first calling England "onii-chan" and later telling him that they're not brothers anymore.
Hungary and Austria were like this towards North Italy when he was a young child. Also Spain, to South Italy.
In Shoulder a Coffin Kuro, the titular heroine and her sidekick come across a pair of very young and very naive twin girls and bring the two along on their journey. They find themselves having to run herd on the kids quite a bit, as well as teaching them about the outside world.
Pokémon is especially bad about this, with insane amounts of one-shot characters clearly being raised by a (often same-gendered) grandparent. With the original main cast, we also had Brock who experienced doubleParental Abandonment, and got promoted to parent for all of his younger siblings. Reversed with Misty, whose parents are mysteriously not in the picture and her older sisters are the ones who got the promotion instead and they're not good at it at all. Also, Gary is the only recurring character to have the "raised by a single grandparent" thing. Fleshed out a bit in the manga, where it's revealed that both his biological parents are dead.
Of the main protagonists, only May and Max have both their parents, but Brock and Cilan do have siblings. Of course that's something that's recurring with the games as well.
Happens a lot in One Piece as most of the characters are orphaned or abandoned at a young age. The most powerful example would have to be Nami's foster mother Bellemere who sacrificed herself for her daughters because she refused to deny that they were hers.
Tons of others worth noting, though. It happens so often it practically invites you to speculate on what Oda's childhood home life was like.
Luffy towards Shanks, since his father's busy with his "job", and his grandfather is a well-intentioned yet really bad parental figure. They were so close, many thought they would be revealed as actual father and son. Luffy and Ace both also had a foster mother (Curly Dadan) in their youth, again because Luffy's dad was gone and his grandpa simply couldn't it in parental-like shoes despite deeply caring for them. Ace also finds this with his captain Whitebeard, since his father, whom he deeply resented anyway, is dead.
There's also Sanji and Zeff, Robin and both Clover and Saul, maybe Zoro and Kuina's father, Chopper and Hiriluk... in fact, the only two members of the main crew that don't appear to have ever had a parental substitute of some sort are Usopp and Brook.
In Vampire Knight, Yuuki has Cross as her adopted father and to an extent, also Kaname. Kaname is her brother, however. Sort of. It's... complicated.
In the Captain Tsubasa manga, Misugi's girlfriend Yayoi (who is stated to be a nursing student in university) temporarily becomes this to Hyuga's younger siblings when Hyuuga's mother becomes seriously sick and, due to his conflicts at work, he can't take care of them.
The Baba Yaga arc of Soul Eater revealed that Sid took in Black Star after the Star Clan was destroyed by Shibusen. However, not much has been made of this relationship in a parent-child sense, though it's evident Sid looks out for Black Star. If his methods do seem alittle odd at times. The reveal made sense, given the attitude towards Black Star taken by both the meister and his partner Nygus.
Continued in principle by Black Star taking Angela back to Shibusen. More likely to be 'big brother' than 'parent' given the age difference, but Shinigami agreed she'd be looked after, and most importantly the thought was there.
Kyousuke, his anti-villain counterpart, is this even more for his followers, at least those who are still pre-adolescent.
Oboe is this for Hamel in Violinist of Hameln. It is not obvious for a long, long time, thanks to the Hamel's extreme Jerkass Facade and Oboe mostly keeping in the background (not without a reason), but in the end Hamel even directly states that Oboe is only being he'll ever call "father" when confronting his Big Badbiologicalparent.
Bear in .hack//Sign is pretty much the Team Mom. In the real world, he grieves at his broken relationship with his own son, and in the end of the series becomes Tsukasa's real self legal guardian.
Although Nagi wishes he were more of a boyfriend, Hayate seems to be playing this role for her in Hayate the Combat Butler. Maria is her mother figure, though the role originally seemed to be that of big sister.
Hinagiku and Yukiji found the Katsura's to be both willing Parental Substitute and get to play the Happily Adopted card when their parents dropped a large debt on them and disappeared.
In the character profiles, Sakuya is said to have been raised by her two butlers and her nurse, instead of her parents, while also serving as the parents to her siblings.
In Fullmetal Alchemist, it's mentioned that even before their mom died, and especially after, the Rockbells' home was a home to the Elrics' as well.
Izumi Curtis also seems to consider the Elrics to be surrogate sons... not that this means she's ever going to go easy on them.
The better members of the Amestrian military embody this trope for Ed and Al. These relationships are more emphasized in fanfiction, where some stories have one of them, usually Roy, who gets paired with Riza, eventually adopting the Elrics and such.
In Bleach, Kenpachi could be seen as this to Yachiru. She turns out to be the incarnation of his Zanpakutou, however.
It's strongly implied in the last arc that Yamamoto was this to a young Shunsui.
In the Hellsing manga and OVA, Alucard acts a little to a father surrogate and mentor to Seras Victoria, who is orphan and has lived in orphanages since her parents' terrible deaths. Integra Hellsing also fills in as Team Mom on occasion (at the ending is more prominent when literally she lectures Seras as if a child) when she's not having Les Yay with her.
Hell, even the Les Yay moments made her seem motherly; feeding Seras her blood from her index finger as a mother would feed a baby from their...well, nipple. The way Integra spoke to Seras in the manga during that scene was also very motherly.
Misato Katsuragi is definitely this to Shinji Ikari (and to a lesser extent, to Asuka Langley Soryu), although in an unusual variation he seems to end up taking care of her just as often. (And, because this is Eva and things can't be nice and simple, there is a whiff of Unresolved Sexual Tension thrown into the mix....)
Quatre from Gundam Wing has four of these: the four highest-ranked members of the Magnac corps, led by Team Dad Rashid.
Dan'l Baboon from Kimba the White Lion acts as a father figure to the title character.
Daikichi of Bunny Drop acts as the father figure of Rin, the little girl he took in and raised. He also becomes the father figure of a boy named Kouki, so much so that Kouki proudly declares that he would be happy for Daikichi to be his father, and when his mother does remarry, he still considers Daikichi more like his dad than his actual step-father.
Hiko Seijuro XIII can be seen as parental substitute to orphaned Kenshin, who he rescued, renamed and took under his wings in age of 8. Hiko may be too proud to admit it, but it’s clear he cares for his baka deshi and will return from retirement to help him.
Kaoru tries to be this to Yahiko, an ex Street Urchin whom she and Kenshin rescued from being a orderline child slave to low-ranked delinquents. It doesn't always work.
Similarly, Okina was a grand-parental substitute to Misao.
In the Hokkaido arc from the manga, Kenshin and Kaoru are the bio-parents of little Kenji but also play this trope straight for three teens: Ashitaro, Alan and Asahi.
In Yu-Gi-Oh! 5D's, Yusei, Crow and Jack were taken in by Martha when they were young. Crow himself becomes one to several children.
In Gundam Seed Destiny, Gilbert Durandal is maybe Rey's adoptive father, but at least he is a parental figure for both Rey and Shinn. It can be interpreted as manipulation, but he appears to genuinely love them. He actually forgives Ray for shooting him, as in "forgive just before dying".
In Magical Girl Lyrical Nanoha, some time before the action started, Precia'sCatgirl familiar and house maid Linith/Rynith took this role for Fate, showering her with the love that she didn't get from her psychoticmother. Linith eventually died, fading away after her contract to train Fate and make Bardiche is fulfilled.
There is a discussion between the two children adopted by Fate Testarossa-Harlaown regarding adoption and how they view their guardians. Admiral Lindy Harlaown became Fate's adoptive mother, but Caro decides that after being adopted by Fate that she's like an older sister. When Erio is asked whether he considers Fate more like his mother or his sister, he can't decide.
Well, strictly speaking Erio thinks of Fate as a mother from his reaction. He's just too embarrassed to say that to Caro. Especially given that she's his aunt by adoption (due to Fate being too young at the time to adopt her officially) and he's attracted to her.
In the StrikerS manga, he occasionally calls Fate "Fate-nee-san ("Big Sister Fate"," but exclusively refers to her as "Fate-san" (Miss Fate, or simply Fate) in the anime.
Most other characters refer to Fate as Erio and Caro's mother when talking with them. Vivio even believes that she should keep her distance when Erio and Caro spend time with Fate, because she has two mothers while they only have one, but they suggest that she does not need to do that.
Not to mention, there's Mad Scientist Jail Scaglietti referring to Fate as Erio and Caro's mother during his horrifying Hannibal Lecture towards her, in which he accuses her of raising them as Child Soldiers and being Not So Different from Precia. Luckily, Erio and Caro don't agree and tell Fate it's all right, which reassures Fate and lets her beat the shit out of Jail.
Furthermore, Nanoha pretty much ends up as Vivio's mother by virtue of being the first one that treats her like the scared little girl she is, with Vivio doing the promoting by clinging desperately to her almost all the time at first.
And let's talk how Hayate Yagami "getting and adapting" her new "family" in A's. She even explicitly refers to them as her "children," and in Striker S, Hayate, the Wolkenritter, Reinforce Zwei and Agito are referred to as "the Yagami family."
Sara in Shokojo Sera becomes Lottie's "little mother" for all intents and purposes, as in the original novel. It's stated in the anime that Lottie's mother died when she was very small, though she does have a father who appears briefly in one episode.
In Ai Yori Aoshi, Aoi's mother took Miyabi Kagurazaki in after her parents, who had long served the Sakuraba clan, died in a car accident, and considers her as her other daughter. Miyabi officially gets adopted in the Distant Finale.
Demon Slayer: Kimetsu no Yaiba has Kagaya Ubuyashiki, the Big Good of the story, exhuding such Team Dad vibes that some cast members consider him a father figure. Including one that is older than him.
The once Water Hashira, Sakonji Urokodaki, is this to the main character Tanjiro, his little sister Nezuko, and to his successor Giyu Tomioka. Similarly, Zenitsu Agatsuma considers his master and once Thunder Hashira Jigoro Kuwajima as his "adopted grandfather".
Shinobu Kocho, the Insect Hashira, is a milder version of this (mixed with Benevolent Boss and Cool Big Sis) to the nurse girls from the Butterfly Mansion. She's also this to the once Wild Child Inosuke Hashibira, which is a plot point later: finding out about her death in battle helps him trigger and recover his lost memories of his actual mother.
In Inuyasha, Sesshoumaru may have taken in the orphaned Rin as his companion but was more of an Aloof Big Brother figure to her. The one who actually did the brunt of her raising was Sesshoumaru's manservant Jaken, and it's even adressed in one of the OP's where Rin happily chases Jaken around and plays with him while Sesshoumaru stares from a distance.
At the tome the manga finished, Rin was seen living with Kaede
The sequel, Hanyou no Yashahime, has Kagome's now grown-up brother Souta and his wife Moe being this to the three titular Yashahime: the sisters Towa and Setsuna (Sesshoumaru and Rin's daughters) and Moroha (Kagome and Inuyasha's daughter) on top of traising their own daughter Mei.
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