In Attack on Titan, Eren Yeager is noted to be a fairly average soldier beyond his high scores in hand-to-hand combat. Since their opponents are man-eating giants, unarmed combat is considered to be a waste of time for a soldier to learn and not considered in their final scores. Cynical Annie mentors Eren in numerous unarmed techniques, which comes in handy later on when he discovers his ability to transform into a Titan. Then it becomes even more vital, when he uses several of the techniques Annie taught him to disable the Armored Titan, a much larger and tougher opponent.
Bleach: Ichigo took karate lessons from an early age, initially because he wanted to be the kind of son who could protect his mother. When he finally became a shinigami, he was therefore already a very competent fighter who didn't need to learn how to fight from scratch.
In Cowboy Bebop Spike had a guy requesting to teach him martial arts, where Spike demonstrates a knife disarm and the philosophy of being calm as water. The guy was having a hard time understanding it all, but in the climactic fight he manages to pull off the same move against a mook. And immediately subverted when he is shot and killed in the midst of his celebration.
The first episode of Diebuster shows Nono accidentally splitting a plate in half with absolutely no effort. She mentions, almost as a throwaway joke, that she's good at splitting things. Fast forward to the second half of the series. Nono uses that same power to completely bisect Saturn's moon Titan and then later a freaking black hole, which even the characters admit should be impossible.
King Kai teaches Goku the Spirit Bomb, and outlines exactly what kind of power this attack has. Not only that, but he says only to use it as a last resort. So Goku has to use it in his following battle as well as nearly every movie and future Big Bad.
It's okay though. It may have all the power of life, the stars, and the universe, but it never works anyway.
Except on Kid Buu. At the end of the series.
After unlocking Super Saiyan, Goku no longer uses the Kaio-Ken (also taught to him by King Kai) because even the original Super Saiyan form provides two-and-a-half times as much power for a much smaller drawback. He does use it once in Anime Filler, combining it with his Super Saiyan form. Even so, he only manages to do this because, in the other world, his body does not have the same limitations and even then the combo nearly depletes him fully after a few seconds. Not counting this one instance, Goku doesn't use the Kaio-Ken for over seventeen years before he manages to combine it with his Super Saiyan Blue form and uses it during his battle against Hit.
In Fairy Tail Gray learned how to handle himself in a motorcycle chase against Racer, and can strip in a split second. In his fight against Sugarboy he steals a motorcycle to pursue him and and dodges an attack by taking off his jacket quicker than the eye can see
In the second episode of Fate/Zero, Kiritsugu practices reloading his Thompson Contender, noting that the process takes about two seconds. This speed is put to the test twenty-two episodes later during his final battle with Kirei, where on two occasions he needs to reload the gun before his opponent can get back into melee range.
In Part 3 of JoJo's Bizarre Adventure, in the very first episode, Star Platinum is able to bring Jotaro assorted objects without him moving. This power is later used to psych out Daniel D'Arby in his poker match with Jotaro making him doubt his own cheating.
In Part 4, Josuke learns how to use Crazy Diamond to shoot projectiles at an enemy Stand user. He later uses a variation on this same skill in his climactic fight against Yoshikage Kira.
In Kemonozume, Bon sadly mentions that his Flesh Eater arms prevent him from achieving his dream of being a shot putter. Near the end, when Toshihiko and Yuka need Ooba's eyes to stop the giant rolling ball, Bon picks up Ooba's head and shot puts it back to them.
Yuka also uses the paralysis technique Toshihiko taught her on Toshihiko, to stop him from following her in the last episode, but it doesn't last long enough to work.
The fights in Kenichi: The Mightiest Disciple often feature Kenichi, at a critical moment, using a technique taught to him in the last training session shown.
And occasionally bringing back old techniques from earlier in the series, such as the yamazuki double punch. Other characters make particular note of whenever he uses the "kouhou - haihou" stepping method, as it was the first technique he was ever taught. This isn't So Last Season either: the techniques usually remain just as useful as they were the first time.
And then there's Area Search, a utility spell Nanoha created way back in the third episode of the first season to solve a specific problem and has never had the chance to use again...until the second-to-last episode of the third season, which gave the hidden Quattro a very nasty surprise.
A more far-reaching example; in volume 3, Negi uses a bunch of magical decoy spirits during his fight with Evangeline. 200 chapters later he pulls out a much larger scale version of the same technique to fight Kurt Godel.
During the fight between Negi and Rakan, Jack mentions that now several people in the world know how to effectively battle Negi's Thunder God technique. Guess which elemental Averruncus Fate ends up fighting?
Nina is shown innocently practicing Aikido. Later, when Tenma is attacked, it comes in handy.
Dr. Reichwein is shown on an indoor jogging track while mulling over a case. This helps when he has to chase down two hoodlums at a dead sprint.
Naruto has the titular character walking into a person practicing a ninjutsu technique (naked); we can tell it's Hinata, but he can't, becausehe'sNaruto. She uses this at the end to kill a bunch insects the enemies were attacking with.
She is shown earlier training with the technique; she activates her Byakugan, some kunai fly at her, and within moments all of them are on the ground, broken.
Naruto himself debuts the series unable to use his (second) most famous technique (the most famous being the Sexy no Jutsu)
There is the most famous Sennen Goroshi (Thousand Years of Death) which was introduced for comedic effect, but Naruto uses it differently during his battle against Gaara. Apparently he thinks that is obviously the technique to use in that situation, and belives that Kakashi taught him that technique.
Naruto's Rasengan ability counts. At first it seemed like just another technique in Naruto's arsenal that he would use to defeat the current arc's villain. Thing is, it becomes his signature technique near the end of the next arc when he enters a famous clash with its counterpart, Sasuke's Chidori.
Sasuke's shadow shuriken technique gets used again during his fight with Itachi, although he modified his shuriken to avoid a repeat of having his enemy dodge it harmlessly.
Naruto's ability to share experience and chakra with his clones receives this treatment twice over. First he realizes it can be used to gather extra nature chakra while he's in combat and later it's the entire basis for his ability to create a chakra network with his allies.
Naruto also uses this to maximize his training time. If a technique takes one hundred hours of practice to master, then it will take one hour for himself and ninety-nine clones to learn it.
In the first chapter of One Piece, Shanks scares a sea monster away by staring it down. Over 400 chapters later this is revealed to be an actual superpower called Haki, and comes in three forms (Their names change depending on the translation, but the following names all come from the Viz translation, for clarity's sake). There's the Color of Arms Haki which allows their users to bypass Devil Fruit users' Nigh-Invulnerability, the Color of Observation Haki which allows one to sense others' presence and anticipate their attacks, and the aforementioned power to knock people out, the Color of the Supreme King. The first two types are common to everyone and can be awakened with proper training, but only a select few possess the third type, Luffy being one of them.
In the episode "Noodles, Roamin' Off!", Team Rocket breaks up and each pursues their own goals before reuniting in the end. Oddly, everything they do comes back to help Jessie earn her third ribbon in the later episode "Dressed For Jess Success". Jessie decides to develop her Jessilina role and distances it more from her own career in Team Rocket...thus turning it into a role that anyone can play, including James. Meowth's natural talent for making ramen noodles wins him the appeal round. And James's fearless battle style against a far greater foe, though only infuriating his opponent before, pays off when his Carnivine throws Dawn's Mamoswine completely off its game and causes it to go berserk, costing it points with the judges and winning him the third ribbon.
Meowth's potential culinary skills would continue being developed throughout later episodes. He would end up winning several appeal rounds for Jessie in the Kalos showcases and in the "Eevee and Friends'' short, he even acts as cook for the Eeveelutions' party.
Team Rocket are actually pretty proficient with this trope. A lot of their tricks or skills they learn for a failed square off against Ash's team end up coming in handy for them in some form otherwise. They're experienced with nearly every line of work known to man as a result of using them to shadow the twerps.
In Pokémon Special, Lady Berlitz tries her hand out in many new things, so it's inevitable that some of them would come in handy. One good case is that by becoming a whiz at the slot machines, her eyes become very skilled at keeping up with fast objects. She manages to defeat Maylene's Riolu despite it jumping around behind a wall of falling rocks, and later has an easy time at the Battle Arcade by always landing on favorable results.
Occurs in Ranma ˝ during the moxibustion storyline. Cologne teaches Ranma a new technique so he can fight back against Happosai without strength, a technique which requires Ranma to stay calm and not emotionally react to his opponent. Genma, his father, immediately tries to get a rise out of him with "Humiliating Photo Fu," whipping out embarrassing naked baby pictures. The whole sequence seems like an extended riff on Genma's usual Jerk Ass tendencies...but Ranma actually puts Humiliating Photo Fu to use during the climactic battle against Happosai, by flashing photos of himself as a girl in lingerie.
Also, moves that characters learned throughout the series are often used later.
Sgt. Frog: The Great Resonance, which the Keroro Platoon discovers completely by accident in episode 155, is used to power up the God Keron's final attack against the Keromet in episode 203.
Slam Dunk is called after a sort-of Chekhov's Skill: it's one of the most spectacular moves ever in basketball and Sakuragi decides to make it his own. It takes him quite a while to master it, but it becomes very handy in the second match against Ryonan, where Sakuragi scores a magnificent one to give the victory to Shohoku.
Similarly, Captain Akagi spends half an episode teaching Sakuragi how to do rebounds. Sakuragi eventually becomes so good at this specific move that it becomes his other signature skill, and it's vital to the team in the match against Shoyo.
In Subaru, her spending the previous two years mimicking everyday occurences and acting out various human and animal roles gave Subaru a perfect basis for dancing and learning ballet.
In Summer Wars, a lot of the Jinnouchi family members have skills or positions that end up becoming relevant to the fight against Love Machine. The most important, though, are Kenji's math abilities and Natsuki's Koi-Koi skills.
In YuGiOh The title character Yugi is really, really good at puzzles. His ability to solve one nobody has completed in five thousand years jump starts the entire series by unleashing his Dark Counterpart Yami. It also plays into his duelling ability, and it seems significant that, in his final duel of the series against aforementioned counterpart, his deck includes a number of toy and puzzle based monsters.
Anzu Mizaki is established as training to be a professional dancer. In the early Manga, her ability to count beats and measure rhythm saves their lives in one of Kaiba's sadistic games involving heavy blocks plummeting down towards the group as the blocks are falling in a set pattern that she can keep track of.