In the manga
In the Be the Best! Pokémon B+W manga
Pokémon Ranger's Zebstrika activating Lightningrod in Be the Best! Pokémon B+W
Monta's Roggenrola activated Sturdy in The Key to Triple Battles.
A Pokémon Ranger's Zebstrika and Monta's Excadrill activated Lightningrod and Sand Force in The Battle for More Friends!.
Dol's Bouffalant activated Sap Sipper in Challenge the Battle Subway!.
Monta's Watchog activated Illuminate in Let's Master Pokémon Capturing!.
Monta's Victini was unable to activate Victory Star in The Birth of the Best Pokémon Trainer! since the Serperior Cheren borrowed used Gastro Acid.
In the movie adaptations
Darkrai activated Bad Dreams in The Rise of Darkrai.
Xerneas activated Fairy Aura in Diancie and the Cocoon of Destruction.
In the Pokémon Adventures manga
Ruby & Sapphire chapter
Brawly's Makuhita activating Thick Fat in Pokémon Adventures
Parallel to their introduction in Generation III of the video games, Abilities were first introduced in the Ruby & Sapphire chapter of Pokémon Adventures.
During Sapphire's battle with Roxanne in Blowing Past Nosepass I, Roxanne's Nosepass proved superior to Rono. Worried that Rono would be defeated, Sapphire attempted to switch Rono out for Chic but was unable to. Roxanne explained that because her Nosepass has Magnet Pull, Steel-type Pokémon cannot switch out. However, Sapphire figured out in the next round that she could use this to her advantage because Nosepass's magnetic attunement causes it to automatically face north when idle. While Roxanne was bragging about her impending victory, Nosepass let its guard down, allowing Rono to sneak up behind it from the south and land a devastating hit that caused Nosepass to faint.
Ruby's first encounter with Abilities arrived in Stick This in Your Craw, Crawdaunt II when he and Mr. Briney were attacked by a wild Crawdaunt. Peeko tried to defeat it with Quick Attack, but the Crawdaunt's Shell Armor prevented it from doing much damage at all. After Mr. Briney fell unconscious, Ruby had Kiki use Double-Edge and infatuate Crawdaunt with its Ability Cute Charm.
Sapphire later also struggled against a potent counter Ability when she faced Brawly in Mashing Makuhita. After Rono was quickly defeated by Brawly's Makuhita, Chic used Flamethrower against Makuhita, but it had little effect due to its Thick Fat.
While on their way to Slateport City, Ruby and Sapphire were attacked by Courtney and Tabitha at the Abandoned Ship during Adding It Up with Plusle & Minun II. They escaped with the help of a wild Plusle and Minun after Ruby realized that their complimentary Abilities Plus and Minus greatly amplified their power when they fought together.
After Wattson is captured by the New Mauville generator, Sapphire devised a double battle strategy using his Electrike in Plugging Past Electrike II. While Electrike did not have the moves to defeat the generator itself, and the wild Donphan that Wattson and the Trick Master had originally intended to capture would be quickly eradicated by its powerful attacks, Electrike's Ability Lightning Rod would allow it to redirect the bolt away from Donphan, buying Donphan enough time to destroy the generator with Rollout.
Archie's Walrein activated Thick Fat during battle with Maxie's Camerupt in Walrein and Camerupt.
Norman's Spinda was revealed to have Own Tempo as its Ability in Rayquaza Redemption I but Skill Swapped it with his Slaking's Truant.
FireRed & LeafGreen chapter
Red's Aero activated Rock Head while using Take Down in Double Dealing with Deoxys. In the same chapter, Blue's Rhydon activated Lightning Rod.
Red's Poli activated Damp in Put Your Beast Foot Forward. It was Skill Swapped by Organism No. 2 in Storming the Forretress.
Blue's Alakazam copied Chuchu's Static with Role Play in Secrets from Sneasel.
Emerald chapter
Emerald's borrowed Phanpy had Pickup in A Dust-Up With Dusclops.
Diamond & Pearl chapter
Diamond's Lax had Pickup in Stagestruck Starly.
A wild Hippowdon had Sand Stream in Bombastic Bibarel & Heroic Hippopotas.
Cyrus's Magnezone had Magnet Pull in Problematic Probopass and Mad Magnezone II.
Diamond's Kit was revealed to have Own Tempo as its Ability in Well Met, Weepinbell but couldn't activate it since Sebastian's Weepinbell cancelled it out with Gastro Acid.
Platinum chapter
A Tyranitar belonging to the Battle Factory had Sand Stream in Outlasting Ledian.
HeartGold & SoulSilver chapter
In All About Arceus IV, Arceus activated Multitype.
Black & White chapter
Brycen's Vanillish had Ice Body in The Cold Hard Truth.
Brycen's Beartic activated Snow Cloak in A Cold Reception.
Black's Costa activated Solid Rock in One Way or Another but Iris's Haxorus negated it with Mold Breaker.
In the Pokémon Battle Frontier manga
Enta's Vulpix activated Flash Fire in Enta Arrives at the Battle Frontier!.
Enta's Feebas activated Swift Swim in Introducing the Frontier Brains!.
When Enta battled Lucy's Seviper with Zangoose in The Predestined Battle!, Zangoose activated Immunity to prevent itself from being poisoned.
In the Pocket Monsters BW: The Heroes of Fire and Thunder manga
Togari's Watchog activated Keen Eye in FAT1.
In the Pocket Monsters Diamond & Pearl manga
Electivire was shown to activate Motor Drive in Ash's imagination in PDP07 if Pikachu used Volt Tackle on it.
In the Pokémon Diamond and Pearl Adventure manga
Saturn's Rhyperior activated Lightningrod to redirect Hareta's Luxio Electric-type moves to it.
Hareta's Riolu has Steadfast which activated after flinching from B-2's Drapion.
Hareta's Piplup has Torrent, which powered up its Water-type moves.
Hareta's Luxio activated Intimidate in A Novel Test!! on Candice's Regirock and Regice but Regirock's Clear Body prevented Intimidate from working. Regice and Registeel were revealed to have Clear Body in the same chapter but weren't shown activating it.
Hareta's Regigigas has Slow Start, which proved to be a disadvantage for Hareta.
Koya's Absol's Super Luck nearly defeated Hareta's Empoleon but a comeback with Empoleon's Surf would have given Hareta the win but the battle was interrupted by Mitsumi's Glaceon's Ice Beam.
Koya's Mamoswine activated Snow Cloak during a hailstorm.
In the Pocket Monsters Platinum: Aim to Be Battle King!! manga
In PBK1, Shin's Bronzong had Heatproof to minimize the damage taken from Yū Shirogane's Infernape's Fire-type moves but Infernape's Blaze powered them back up.
Yū's Scizor received Heatran's Flash Fire Ability after Bronzong Skill Swapped them in PBK4. Yū's Bronzong had Levitate in that same chapter.
Yū's Regigigas had Slow Start in PBK7.
In the Pokémon Pocket Monsters manga
Norman's Slakoth activated Truant in I Won't Let You Lead.
Zorua and Zoroark activated Illusion in PMHGSS20.
In the Pokémon - The Legend of the Dragon King manga
Taichi's Ampharos had the Ability, Static.
Source