In the Age of Fire series, each of the three main protagonists gets one at some point or another after their parents are killed and they're scattered as hatchlings: AuRon had NooMoahk (the elder dragon who served as his mentor during his last drakehood years), Wistala had Rainfall (the elf who raised her most of her life), and RuGaard had FeHazathant (who took pity on him and adopted him into the Lavadome's Imperial Line when he arrived), respectively.
AuRon himself was in turn one to Heiba, the orphaned human girl he was tasked with protecting until he could get her back to her own kind, which took long enough that they ended up bonding closely.
Madame (a.k.a. The Old Lady) in Babar took the role of Babar's mother after he gets lost in Paris, raising him and paying for his education creating a strong bond among them. This is expanded in the animated series.
In The Baby-Sitters Club, Claudia's grandmother Mimi was this to both Mary Anne (whose mother died when she was very young) and to Claudia (whose parents are alive but don't really "get" her).
Subverted in Brotherhood of the Rose, by David Morrell. The two protagonists meet in an orphanage from which they're recruited by CIA chief Elliot, who presents himself as a surrogate father figure. They later discover that Elliot (and other members of his worldwide conspiracy) have done the same thing with other orphans, in order to create a team of Elite Mooks who'll obey their orders without question.
The Brothers Karamazov: Fyodor Karamazov cares little for any of his three sons; young Dimitri goes half-naked and unfed until Grigory steps in and virtually raises him himself; Ivan and Alexei are adopted by their uncle Miusov.
After her parents go to war in Dirge for Prester John, Sefelet is cared for by Vyala, her mother's friend's mother. They appear to bond more than Sefalet did to her real parents.
In Fire and Hemlock, Pollys grandmother is her parent substitute, as her own parents are in an unhappy marriage and fight a lot. They divorce later in the novel There is also Mr. Lynn and to a lesser extent his friends, who treat Polly more like a friend, but still qualify, as they readily step in when Polly's actual parents neglect her and her grandma is not nearby.
In Gene Stratton-Porter's Freckles, Freckles acquires two: Mc Lean is a father figure, and Mrs. Duncan as a mother figure who assures him that she loves him like a son and weeps over how desperately he needs the affection.
In the Goosebumps book A Night in Terror Tower, Morgred the sorceror is set to fill this role for Edward and Susannah when they finally escape into the future to live new lives away from their evil uncle and the High Executioner. As the late, rightful King's court mage, he promised to protect them from harm.
Nearly every adult who has any interaction with Harry is a Parental Substitute They range from mentor/grandfathers like Albus Dumbledore to doting/supportive uncle figures like Sirius Black (who is also his godfather), Remus Lupin and Hagrid. Minerva McGonagall was the head of his house so there's definitely an element of this trope there. Arthur and Molly Weasley basically became his parents once he got away from the Dursleys. Because this is Harry Potter, things don't end well for the first three.
Harry's friends are not immune either. Neville Longbottom is raised by his grandmother due to his parents having been tortured to madness by Death Eaters. Harry himself also becomes one to Teddy Lupin. Although he seems to be living with his grandmother, he often visits the Potter-family.
More stories of this are told for reoccurring background characters. Susan Bones seems to have been raised by her aunt as nearly her entire family were killed by Death Eaters.
Bush towards the decade-younger Hornblower in the Horatio Hornblower books, evolved out of a Big Brother Instinct from early in their careers; he's constantly worrying that his captain isn't getting enough rest or credit or human contact and Hornblower compares him to a mother hen at one point. Not that Bush quite realizes this since he's Britishly out-of-touch with his own emotions.
Celia and Tam Lin in House of the Scorpion who are Matt's caretaker and bodyguard respectively, are pretty much his Parental Substitutes, since being a clone, he has no parents, unless you count his original's parents, which would be technically, but they have been dead for over a century.
Jim could be seen as this to Huckleberry Finn, whose own father is a violent and uncaring drunk.
Haymitch develops this kind of relationship with Katniss and Peeta in The Hunger Games.
In Andre Norton's Ice Crown, the princess was raised by her grandfather. Roane appears to be in her uncle's charge, though he seems more taken with the notion of another pair of hands with less regulation, since she's related.
In The Infernal Devices, Charlotte raised Will, Jem, and Jessie since they came to the institute. Will says that she would have been called a governess had she not been so intelligent and if she didn't have the ability to chop one into pieces.
Jeeves and Wooster: Since the issue of Manchild Bertie Wooster having parents is never dwelt on, there are plenty of implications that he regards Jeeves as something of a father figure. Jeeves, for his part, is often noted to cast a "paternal" eye on Bertie's antics.
In Edgar Rice Burroughs's The Chessman Of Mars, U-Thor received a slave woman from his jeddak; he freed and married her, and regards the son she bore the jeddak, A-Kor, as like a son to him. When the jeddak, a Royal Brat, has A-Kor imprisoned out of fear and envy, U-Thor demands an accounting.
I have made of her a free woman, and I have married her and made her thus a princess of Manatos. Her son is my son, O-Tar, and though thou be my jeddak, I say to you that for any harm that befalls A-Kor you shall answer to U-Thor of Manatos.
Also, in the earlier books Gods of Mars and Warlord of Mars Tars Tarkas, Tardos Mors, and Mors Kajak are implied to have served this role for John Carter's son, Carthoris, after Carter was returned to Earth.
J. R. R. Tolkien's The Lord of the Rings and The Silmarillion feature many parental substitutes: Bilbo (for Frodo), Théoden (for Éomer, Éowyn and arguably Merry), Elrond (for Aragorn), Maglor (for Elrond and Elros), Annael (for Tuor), Thingol (for Túrin) etc. Maglor's fostering of Elrond and Elros is perhaps especially notable in that Maglor had been (twice, reluctantly) involved in the slaughter of the boys' family before that, and that he had contributed to their mother's attempted suicide...
In Loyal Enemies, Rest spent most of his childhood as a poor kid whom nobody wanted to care about, constantly kicked out of every apprenticeship he tried. Then Veres (badass monster hunter Magic Knight) came, said the kid has a magic gift and took him on as his student. At the end of the book another wizard mistakes them for father and son. Rest corrects him, but states that he'd be proud to be Veres' child and he regards the wizard as a substitute parent.
In Malevil, the main character Emmanuel is adopted by his uncle Samuel after he runs away from home. Samuel is far more of a father to Emmanuel then his cowardly, hen-pecked brother Simon ever was.
Mirabile is set on a recently-established colony world where there are professional parental substitutes, like the protagonist's friend Elly, who make a living raising other people's children alongside their own. The protagonist explains that the "population is still so small we can't afford to lose genes just because someone's not suited, one way or another, for parenting".
In The Mortal Instruments, Luke helped raise Clary along with Jocelyn. By City of Heavenly Fire, they're referred to as father and daughter more often than not by themselves and others. In a way, he was sort of a father figure to Simon, too, as the latter's father died when he was younger.
In Ian Fleming's "Octopussy", James Bond is sent to take a retired officer to justice. The man, working intelligence at the end of WWII, smuggled a cache of Nazi gold home and killed the mountaineer who had led him up to where it was hidden. It's business for Bond, but it's also personal, as he'd been a friend to the dead man, who had taught him to ski as a teen before the war, and was "something of a father to me at a time that I happened to need one."
Alanna of Song of the Lioness first has Old Retainer Coram, who reminds her that he changed her diapers. As a page, she has Myles of Olau, who is such a good replacement father that he eventually adopts her.
The Immortals' Daine is "mothered" by three different women — Queen Thayet, K'mir warrior Buri, and horse trainer Onua.
Kel of Protector of the Small actually has living Good Parents, but obviously they're not around while she's training for knighthood and they're ambassading. Lord Raoul, her knight-master, essentially pulls her through the crappy, 15-18 years. Kel herself becomes a substitute parent to Tobe when she basically adopts him by buying his indenture from an abusive master.
The four main characters in the Circle of Magic series are raised by two women who, after a time, they refer to as their "foster mothers".
A Prayer for Owen Meany: Owen's real parents don't take much interest in Owen, so Johnny's mother pretty much takes care of him. This makes her accidental death at Owen's hands all the more heart breaking.
Halt from Ranger's Apprentice is a father-figure to both Will and Horace. It comes up several times in the books that Will and Halt think of each other as father and son. Similarly, Pauline thinks of Alyss as a daughter.
RCN: Given Cordel Leary's frequent absences from the Leary household due to his political activities, Hogg serves as a substitute father for Daniel, teaching him what it means to be a man.
In The Red Abbey Chronicles, girls who newly join the Abbey usually choose a girl who has been there for longer, and follow her around all the time. Apparently, the Sisters do not formally control this, but encourage it by assigning the same duties to both girls. (The Sisters also serve as parental subsitutes, but cannot focus on one girl; only the very young ones have a Sister specifically devoted to caring for them.)
Dr. Montgomery in A Series of Unfortunate Events is a good example. In The Penultimate Peril, volunteers Kit Snicket and Dewey Denouement answer some of the Baudelaires' questions and the latter offers to become their guardian. All three of them die.
In The Shattered Kingdoms, Lahlil survived an attempt to kill her by exposure and was taken in by the Nomas people, acquiring some parental substitutes. However, some misapplied Nomas religious practices resulted in her being cursed with an illness, and she realised that at least some of them knew the source of her problem but were unwilling to admit it to her. She left, and didn't stay in touch. As such, she's estranged from both birth and adoptive parents.
As part of the same scenario, Sansa's cousin Lord Robert Arryn comes to view her as something between a parental substitute (for his late mother Lysa, who was murdered by Littlefinger after marrying her) and a Cool Big Sis (since Robert believes that "Alayne" is his stepsister).
Running a galactic government and occasionally saving it alongside one's scoundrel husband leaves little time for parenting, as the children of Han Solo and Princess Leia learn. Much of their parenting is done by Leia's longtime friend and aide Winter Celchu.
C-3PO, in a pinch, makes a surprisingly effective babysitter.
The Stormlight Archive: Dalinar Kholin does this quite a bit. At one point he even claims that everyone under his command is part of his family.
After his brother's death, he had to act as a father to his nephew, King Elhokar. Part of the problem with Elhokar's reign is that Dalinar coddles him a bit too much, treating him like a child.
After the climax of the first book, Dalinar starts treating Kaladin as a son, specifically like Adolin. It's just easy to miss because he treats Adolin like a soldier. It comes to a head when Elhokar is mad at Kaladin for derailing the plan to deal with Sadeas. Elhokar wants him executed, but Dalinar flat-out says that if he tries, he'll make Dalinar an enemy.
Jaxon is the closest to a father that Corie and Elisandra have in Summers at Castle Auburn, and he tells them all the time how proud their father would be.
Victor Dashkov to Lissa and a bit to Rose, originally. He acts as a parental figure to both, offering advice and kind words, organizing shopping trips, and buying Rose gifts unavailable to her.
Tasha Ozera is the mother figure to Christian. She raised him herself once his parents were killed. He treats her like his mother and is uncomfortable whenever her love life is discussed.
In the Village Tales novels, the Duke of Taunton is this to his nephews and niece – rather to his sister-in-law's vexation, she being after all their mum, and present, living, and in her right mind. Then again, he is the duke, The Patriarch, head of The Clan, and, most importantly, the man whose lands, money, and titles the eldest nephew will presumptively inherit, so....
In The Westing Game, Flora Baumbach acts as this for Turtle, who is treated as The Unfavorite by her actual mother. Baumbach's own daughter died years before the story started, and it is heavily implied that Westing paired Flora and Turtle together with the intent of invoking this trope.
In The Witches of Karres, Captain Pausert fills this roll for Goth and The Leewit while they are sailing with him.
Thomas Cromwell sometimes thinks back on the late Cardinal Wolsey not just as master and mentor, but as a father. Wolsey certainly treated him with more regard and affection than Walter Cromwell ever did.
Cromwell ends up as a stand-in father to a lot of people. Initially there's his ward Rafe Sadler, who becomes his right-hand man in court intrigues. His nephew Richard takes the name Cromwell after his own father's death, explicitly saying "you are my father now," and an elderly family friend tells Cromwell to look after his wayward adult son. Cromwell also steps into this role for his young nieces as their guardian and looks out for their marriage prospects. Also, any poor but intelligent boy in the vicinity of his London home ends up living there (at one point he has a whole choirful of them) because he's mindful of how he went from Putney urchin to King's right hand and is eager to give other young men the same chance.
In Wuthering Heights, Nellie Dean serves as a parent to the second generation. As both children lost their mothers practically in childbirth, Nellie is the only mother either has ever known.