In Dan Abnett's Warhammer 40,000 novel Titanicus, Golla Ulduna is introduced as a midwife, to emphasize the insanity of her being called up as part of the tertiary reserve. But when they find a princeps in the ruins of his engine, Golla is able to get him breathing air again, just as she would get a baby breathing.
Robert A. Heinlein is rather fond of this trope. The skill in question is usually some sort of mechanical engineering, which the main character does as a hobby, but ends up saving his life later.
One particular example is the premise for the novel. In Have Spacesuit, Will Travel, the main character wins the titular suit in a contest. He spends his free time from then on making it space-worthy, and gets it fully operational just in time for him to be the Right Man in the Wrong Place to save all of humanity.
At the beginning of the second The Wheel of Time book, Lan is giving Rand training in swordfighting, and insists to never use the "Heron Wading in the Rushes" technique — a stance lifting your sword high, that leaves yourself open to attack so that you have a chance to strike.
Turns into a real problem when shortly there after, Lan tells him of the technique "Sheathing the Sword" taking an attack so you have a chance to strike.
A Chekhov's Skill in the making, Mat, Thom and Oliver are constantly seen playing Snakes and Foxes, a kids game, which Mat is openly dismissive of. By the end of book 11 it has become clear that the game is an instruction manual for invading the world of the Finn and defeating them, which those three are well on their way to doing to save Moraine.
Happens many times in Harry Potter, usually in regards to an important spell they need to learn.
Any specifically named spell, even from the Unforgivable Curses from the Bad Guys, eventually gets used at least once during a key event.
A good non-spell example is Ron's skill in chess. Sadly it isn't mentioned much after the first book.
Also Harry's superb flying and Snitch-catching skills make appearances throughout the series, usually with the line "Harry wasn't the youngest Seeker in 100 years for nothing."
Ancient Runes is one of the many electives Hermione is mentioned taking. In the seventh book, She translates The Tales of Beedle the Bard from runes, leading them to the story of the Deathly Hallows.
Harry being a Parseltongue. Him being able to speak the language of serpents appears in The Philosopher's Stone as an example of all the weird things happening around him. Since it doesn't come up again in the rest of the book, one could think it was nothing unusual in the magical world. However, in The Chamber Of Secrets, Harry learns that this ability is extremely rare and only previously appeared in descendants of Salazar Slytherin. The skill ultimately allows Harry to enter the Chamber and fight the basilisk inside. More importantly, it is later revealed that Voldemort possessed this ability and inadvertently passed it on during his first attempt to kill him. Thus, Harry being a Parseltongue helped to slyly foreshadow that he was one of Voldemort's Horcruxes all along.
Severus Snape is given the job of teaching Harry the skill of Occlumency in Harry Potter and the Order of the Phoenix, the ability to shield one's thoughts from the magical mind-reading ability of the series villain, because Snape is known to be exceptionally good at it. In the next book, Snape is revealed to be a traitor working for the villain... until the final book, where Snape is revealed to have been a Good All AlongDouble Agent; the villain was stated to be exceptionally powerful at mind-reading, meaning that Snape's skill at Occlumency was crucial in keeping his true allegiance hidden.
Every other The Hardy Boys novel had Chet Morton take up some hilarious new hobby, such as ventriloquism or shot-putting. These skills would always come in handy by the end of the book, and would never be referenced again in any later books.
It's learned quite a while before the book, but in The X-Wing Series Face, a former child actor, was stated to have lived on Lorrd for a while, a planet whose hat was body language and the reading of such. He uses what he picked up to Sherlock Scan how people walk. This does come up again.
Subverted in the first Xanth book: Bink learns some throws from Crombie before the two part ways, and in a confrontation with Evil Magician Trent, uses one. Trent, an experienced warrior, counters expertly, while politely pointing out that amateur moves like that just don't work on a skilled opponent.
Justified in A Prayer for Owen Meany. Owen is too short to dunk a basketball effectively, but he's so lightweight that when he jumps into Johnny's arms Johnny can lift him high enough for a proper dunk. Owen insists that the pair practice this, and that what matters is being able to do it in under three seconds. (The narrator also finds out later that Owen was practicing how to perfectly pronounce a specific Vietnamese phrase). As it turns out, Owen is Dreaming of Things to Come, and he knows exactly what situation this will be useful for.
In Simon Birch, the extremely loose movie adaptation, the Skills are, instead: "holding your breath underwater for an extended period of time" and "almost supernatural ability to command other kids", both of which become useful for rescuing a bunch of kids trapped in a submerged bus.
Used to good effect in Dealing With Dragons by Patricia C. Wrede. The main character spends the first chapter learning skills her parents think are useless. She spends the rest of the book using those skills to melt wizards with lemony dishwater.
In Matthew Reilly's Hover Car Racer, Jason's Crazy-Prepared mentor teaches him what to do in any situation that might come up in a race, including how to do a manual pit stop if the power is cut off. This skill allows him to cut a 30 second lead in an important race.
The first chapter of Desmond Bagley's thriller The Vivero Letter briefly mentions the hero's hobbies of fencing and SCUBA-diving. The diving later comes in handy for underwater archeology, and at the story's climax the hero kills the Big Bad in a hand-to-hand duel with machetes in which his training in sabre fencing gives him the edge.
In Black Dogs a secondary character reveals that she is a demon, and trusts the protagonist with her true name in case a situation ever arose again where a sorcerer tried to banish her (which happened in a recent fight). Later on in the fight between the protagonist and the Big Bad, in a moment of desperation she speaks her friend's true name and she appears in full-demon form to help deal with the Big Bad's summoned demon.
In Zora Neale Hurston's Moses, Man of the Mountain, when Moses is learning magic from his tutor Jethro he is particularly skilled at summoning large amounts of vermin. Those familiar with a certain other work will realize this comes in handy later in convincing the pharaoh to free the Hebrews.
In the Vatta's War saga, several characters either off-page has learned something, or in the books learns something that turns out to be useful. Examples: Grace Vatta being the company spy and fruitcake maker extraordinaire, and Kylara Vatta having been trained in the military as well as learning how to use fairly exotic weapons, which all turn out to be useful.
In Ranger's Apprentice, Gilan teaches Will how to use two knives to defend himself with a sword and has Horace practice with him. Horace later uses this skill to win his duel with Lord Morgorath when his sword is sliced in half, leaving him with a "useless" sword and a dagger.
In book one of The Sharing Knife, Dag says offhand to Whit that someday he'll teach him archery. In book two, Dag's uncle teaches Fawn arrow-making. In book three, it turns out Whit has been practicing, and Dag gives him more lessons. In book four, Whit buys a crossbow. Towards the end of book four, Whit shoots down a flying malice with a sharing knife that Fawn had converted into a crossbow bolt.
Averted at one point in the Belgariad. Early on Silk demonstrates the ability to alter the appearance of his face through muscle movements. He uses this as a prank on his teammates, and it then never comes up again.
This shows up twice in The Pale King: Leonard's medical knowledge and Toni's ability to not blink for minutes at a time.
All the undersea settlers in Dark Life know sign language. This comes in handy when Ty needs to communcate with a mute man. Justified in that sign language is necessary to communicate while diving.
In the novel My Louisiana Sky, by Kimberly Willis Holt, Lonnie Parker can forecast the weather by watching the behavior of animals. In the novel's climax, he realizes that a hurricane will hit, and convinces his co-workers to shelter the seedlings at the plant nursery where he works in time, so they aren't destroyed.
In Heather Tomlinson's novel The Swan Maiden, Lady Doucette is brought up knowing how to supervise those who care for a castle. This is useful later when she magically builds her own.
In Dorothy Gilman's The Amazing Mrs. Pollifax, Mrs. Pollifax started learning karate from a retired police sergeant. This came in handy several times later on in the series.
Most spells in Septimus Heap are used in this manner: Introduced in the beginning of a book as almost random spells, then used in the climax to plot-deciding effect.
In the A-to-Z Mysteries book The Bald Bandit, Ruth Rose's ability to scream really loudly comes in handy when the Bald Bandit tries to kidnap her.
Ruth Mallory in Someone Else's War has a wide array of culinary knowledge. Early on, she mentions in what is supposed to be a throwaway joke that cassava is poisonous uncooked; if she only had some cassava root on hand, she could trick the LRA enforcers with it. Toward the very end of the novel, the LRA gets relocated to a jungle filled with cassava. Matteo doesn't even realize what's happening when the adults around him start dying.
Chet Gecko in The Charmeleon Wore Chartreuse makes a passing mention of being able to detach his tail. Later, when he gets tied up and hung upside down from the diving board by a school bully, guess how he frees himself?
In Firebird (Lackey), Ilya's habit of speaking with Exact Words to Mother Galina pays off with the Katschei, as does his ruse as the fool, and his learning to stay awake in the face of the Firebird's music.
In No Woman Born, the deceased actress Deirdre is resurrected into a robot body, which thrills her with all it can do. She intends to return to the stage, noting that now she can sing at any range for long as she likes, since her artificial body can't get tired. It also lets her scream loud enough to break windows and put others in pain.
In Joyland by Stephen King, references are made throughout the story of Annie's proficiency with a gun - her teenage years as a shooting champion (good enough to be considered for the Olympics), her ability to clean up at the fairground shooting range despite years of little or no practice, and how her otherwise troubled relationship with her father hinged on her marksmanship talents during their hunting trips together. This, and the fact that she still keeps a gun in her safe despite renouncing recreational use of them, later comes in handy when Dev ends up Alone with the Psycho.
In The Hunger Games sequel, Catching Fire, it is mentioned that Katniss's likes to visit the lake in the woods where her father taught her to swim. Later on this saves her when she is one of the first tributes to reach the cornocopia in the 75th hunger games, because it is surrounded by ocean and she is a strong swimmer.
In the very first chapter of A.L. Phillips's The Quest of the Unaligned, we learn that Alaric is probably the best knife-thrower anywhere in Tonzimmiel. In the climatic final duel the villain has thrown up a shield powerful enough to stop any form of magic, but Alaric's mundane thrown knife completely bypasses it.
In Song of the Lioness, Alanna learns how to fight left-handed when she breaks her right arm in book one. In the second book, she uses this ability to beat a visiting knight who wounds her arm in a not-so-friendly duel.
In Sandry's Circle Opens book, she finds her Pasco dancing over a net to attract fish to it. They use this exact method to catch the assassins later in the book, only with a net made of unmagic.