This is more like Chekhov's Habit, but there's a Running Gag in Hunting The Unicorn of David writing down everything relevant to the Warblers (and especially Blaine). It proves useful when he has hard evidence that Blaine has a stalker.
In the Transformers fanfic series Black Crayons, Ironhide begins teaching Annabelle how to speak Cybertronian. First, it is a cute way to learn about the Twins' pranking plans. Later, it becomes a life-saving skill when she overhears a key piece of information from Starscream.
Jack's ability to memorize fingerprints on things to distinguish them from similar things helps him put out a fire at Dr. Brainstorm's lab in Calvin and Hobbes: The Series.
In the second chapter of A Growing Affection Hinata suggests Naruto work on chakra control by trying to create a tiny Rasengan on each finger tip. This becomes the Five-Points Rasengan jutsu, and shows up multiple times in the story, including the final battle.
Legacy Of The Rasengan: Naruto has KazeKiwa no Jutsu. In this fic it's one of Naruto's signature moves and sees a lot of use. It ends up inspiring Naruto to create the Rasengan since the mechanics of both are similar (no hand signs, spinning chakra, very good chakra control). Also helps Naruto in his fight with Neji since it made it easier for him to concentrate his chakra enough to mimic Neji's fighting style and rip through his Rotation.
Regeneration in Children of Time: Kit Bennett reveals herself as a Time Lord, and the Daleks torture her to study a Time Lord's use of regenerative energy. At the climax, Kit uses a burst of that energy to knock out the Daleks' computers, destroying Dalek Caan in the process. Then in the season finale, baby Katherine, who will grow up to be Kit, heals her dying father and half-dead godfather.
In Break My Fall, Red spends his lunches helping out at the nurse's office. This later becomes important when he has to rush to the nurse's office after school hours to get supplies to treat Green's self-harm wounds.
In Despair's Last Resort, Naomi is established as being the Super High School Level Translator, who knows ten languages. As she's dying, she uses her blood to leave a dying message. But in order to hide it from the killer, she leaves it in French. This allows the one living student who knows French to pick out who the culprit is.
Takara's experience as a journalist helps her out in the investigations.
Kitsune no Ken: Fist of the Fox. During her fight with Kin in Chapter 16, Ino demonstrates that she's got an extremely painful Groin Attack that she learned in order to deal with any perverted men who'd try to hit on her while shopping at her father's store; said attack consists of grabbing the victim's privates and twisting. That tactic proves extremely useful 68 chapters later to deter Aoi's Attempted Rape.
FateBlack Reflection. Rider dreams about Ichigo's fight with Kenpachi in Soul Society through the Command Seal link. The next night, Ichigo displays the ability to handle Berserker easily, to the wonderment of everyone else there. Rider eventually recalls the dream and realizes that the reason Ichigo can fight Berserker so well is because he has experience fighting opponents with overwhelming power and no strategy.
In Katawa Shoujo post-Hanako Good End fanfic Fan Fic/Sisterhood, Hanako attends a first-aid course, the intention being she would be able to put it into practice and use these skills to keep calm in the event Hisao was to have another heart attack, unlike the previous time in which she had a severe panic attack. Instead, she ends up using her skills to save Lilly's father's life after he collapses from a heart attack.
In the Naruto story Eroninja, Yukata makes a puppet that she uses as a sex toy. Her spending months of using it gives her such fine control that during the puppet user tournament, she displays the ability to use her puppet to control another puppet, something previously thought impossible.
The Second Try: In chapter 4, Asuka declares that Shinji will be responsible for the main medical care. In chapter 6, Shinji uses what he's learnt to take care of Asuka during her pregnancy, and delivering their daughter Aki safely.
Deliberately enforced by Kakashi in Team 7's Ascension when he left Naruto a scroll containing water technique. A few months later, he makes Team 7 live in a training ground that has no water at all and keeps them from getting any from outside.