In "The Puppetmaster", Katara learns a particular nasty technique called Bloodbending that allows her to control someone when empowered by the full moon. The episode makes it very clear she does not like the technique. She does use it later, but her willingness to use this technique to torture someone does a good job of showing her vicious side.
Iroh's original technique of redirecting lightning was first demonstrated in the first season with little fanfare. In the early second season Azula demonstrates the ability to actually generate lightning, where Iroh reused that technique against her. This prompts Zuko to request to be trained in the art of lightning bending. After failing to use the regular lightning strike, Iroh teaches him the redirect technique, but refuses to help him practice with actual lightning. Zuko does have to put that training to use over a season later, though not against Azula.
Zuko would also pass the technique on to Aang, who uses it to avoid a fatal blow from Fire Lord Ozai in the finale.
Asami's defense training, which allows her to quickly subdue her father and The Lieutenant.
A unique version occurs in Courage the Cowardly Dog episode "Big Ball Of Revenge", where Eustace had assembled most of Courage's Rogues Gallery to take him out of the picture for good. How does Courage save the day? By screaming for forty seconds straight, with enough force to split the ground beneath them.
In The SimpsonsMovie, Homer has to do a stunt with a motorcycle inside of a spherical cage in order to win a new car. He then uses this same stunt at the end of the movie with the glass sphere surrounding Springfield in order to save the city from a bomb.
In the TOS episode "The Mystery of the Lizard Men", Jonny learns a judo throw from Race Bannon that he later uses on one of the title opponents.
In the series premiere of Jonny Quest: The Real Adventures, "The Darkest Fathoms", Jonny is seen to be practicing how to escape from being tied up. Later in the episode, he is captured by pirates and uses this skill to get free (and save Jessie and his dad while he's at it).
Part Two of The Fairly Oddparents TV movie trilogy "Wishology", Baby Poof is seen watching a ninja film based very loosely on what happened in Part One. Wanda proceeds to turn it off, as it is "too violent for him." During the next few minutes, Poof kicks, punches, and generally bounces around the room. Later, Timmy's friends, family and godparents have all been captured by the Eliminators, who came back from the Darkness, which apparently was only slowed down after Part One. Poof is the only one who can go through the bars of their cell, and when threatened by the Eliminators, he dons a blanket around his head and body, smears eyeliner on his face for a shadow, and proceeds to kick ass big time.
Subverted (hilariously, by the way), where Stan goes through the Training Montage, only to win his climactic ski race with the same two skills he learned near the beginning: pizza, french fries. The actual difference is made when the Meganekko flashes the Jerk Jock and stuns him for more than enough time for Stan to cross the finish line first.
Played straight in a later episode where Randy becomes obsessed with Food Network and Sharon ends up getting a Shake Weight. Her use of it culminates with her giving a handjob to Randy at the end of the episode, curing him of his Food Network fixation.
Parodied in the episode "You Have 0 Friends" with Stan's ability to... roll Yahtzee?
In Codename: Kids Next DoorThe Movie, Operation: Z.E.R.O., Number One has learned a new fighting style which allows him to take down four enemies at once. Each time he is about to use it, he is interrupted. He does eventually get to use it in the finale to take down his agified zombie friends.
In Batman: Under the Red Hood, this is done in reverse with Red Hood cutting the line before it goes taut, and Jason Todd as Robin doing the same thing in a flashback.
In The Tigger Movie, Tigger teaches Roo the "whoopty-dooper loopty looper alley-ooper bounce" (essentially a bounce, but BIGGER), which comes up again near the end when they have to escape from an avalanche.
In Wild Kratts any discussed animal ability gets used to achieve that episode's goal, whether it's to free the animals from Zach Varmitech or just getting their gear back.
In the American Dad! episode "With Friends Like Steve's", Steve expresses utter boredom with all of Stan's CIA tricks like speaking Dolphin and stealing uniforms. After he gets shipped off to a prison camp on an oil rig, Steve uses all these skills to escape.
Turns out Fluttershy has a surprising knowledge of sewing, as evidenced when she was forced to tell Rarity what was "wrong" with her dress in "Suited For Success". This skill allowed Fluttershy and the others to finish Rarity's dress at the end of the episode.
In "Dragonshy", Rainbow Dash is shown playing with a ball and skillfully bouncing it off her head. Later, during the Iron Pony competition in "Fall Weather Friends", she uses her skill to easily win the ball-bouncing challenge.
Twilight spent the entire first season writing reports back to Celestia with what she's learned about friendship. In "The Return of Harmony, Part 2", Celestia snaps Twilight out of Discord's spell... by sending back copies of all her reports, so that reading them will remind Twilight that friendship is worth fighting for.
In "The Crystal Empire Part 1", Twilight is shown to have studied intensely for Princess Celestia's "test", only to find out that instead of an exam, the princess has a mission for her. Later, it turns out that the gravity spell she studied was actually incredibly useful.
In "Bridle Gossip", the Mane Six walk through Poison Joke plants despite Zecora's warning. The effect they have on Fluttershy is causing her to have a deep, manly voice, but it is eventually cured along with the others' ailments. Three seasons later in "Filli Vanilli", Big McIntosh loses his voice the day before he is supposed to perform with the Ponytones singing group. To save the show (and the group's subsequent appearances), Fluttershy drinks a Poison Joke potion from Zecora so she can sing in Big McIntosh's place behind the scenes while he lip-syncs.
In Twilight's Kingdom Part 2, Celestia's reason for sending Discord after Tirek was that he could sense the magical disruption caused by Tirek's Mana Drain. When the Princesses transfer their magic to Twilight, Discord is able to sense it, but doesn't tell Tirek. And once Tirek drains Discord of magic, he can pinpoint Twilight's location without trouble.
In any episode of Cyber Six if Julian shows off a trick of any kind, he will use it to help save the day later on.