I'm nowhere near positive that this list is complete, but I think what I have listed is all I will do. There are links at the bottom that should have at least some of the Pokemon that I'm missing listed.
Pay Day Fearow, Rapidash, and Delibird
Dragon Rage Magikarp
Ancient Power Bulbasaur
Crunch Arcanine
Submission Totodile
Nightshade Hoothoot
Sing Pichu, Pikachu, Spinda, Eevee, and Piplup
Petal Dance Psyduck, Chikorita, Pichu, Igglybuff, Cleffa, and Smoochum
Swift Cleffa
Belly Drum Wooper
Encore Phanpy, Cacnea, Liepard, Pikachu, and Golduck
Metronome Smoochum
Safeguard Natu and Stantler
Double Slap Lickitung
Fire Punch Scrafty and Groudon
Swords Dance Goldeen
Gust Mantine
Whirlwind Swinub
Heal Bell Lickitung
Destiny Bond Sharpedo
Refresh Metang and Pikachu
Mud Sport Psyduck, Corsola, Surskit, and Minun
Follow Me Pichu, Squirtle, and Jirachi
Tickle Igglybuff, Wynaut, and Sableye
Feather Dance Taillow
Teeter Dance Bellsprout, Pichu, Whismur, and Pikachu
Water Sport Plusle and Corphish
Splash Snorlax and Sunkern
Uproar Spoink
Absorb Phanpy
Bubble Magikarp
Charm Pikachu
Wish Farfetch'd, Drowzee, Exeggcute, Lickitung, Chansey, Kangaskhan, Ralts, Absol, and Bagon
Leech Seed Oddish
Sweet Kiss Nidoran♀, Nidoran♂, Poliwag, Bellsprout, Snorlax, Yanma, and Pikachu
Iron Defense Bagon and Normal Forme Deoxys
Bite Lapras
Rage Larvitar and Tyrogue
Agility Magnemite, Voltorb, Hoppip, and Altaria
Light Screen Chinchou
Mind Reader Mr. Mime
Quick Attack Tauros and Charmander
Mist Remoraid and Reshiram
Hydro Pump Dratini and Magikarp
Dragon Dance Charizard
Present Pikachu and Audino
Sludge Bomb Zoroark
Air Slash Suicune and Land Form Shaymin
Howl Charmander and Entei
Nasty Plot Celebi and Deoxys
Zap Cannon Squirtle
Weather Ball Raikou and Bulbasaur
Aura Sphere Raikou
Extreme Speed Raikou, Entei, Suicune, Deoxys, Pikachu, Dragonite, Genesect, and Linoone
Flare Blitz Entei
Crush Claw Entei
Aqua Ring Suicune
Flail Zubat and Eevee
Last Resort Pikachu
Roar of Time Darkrai and Arceus
Spacial Rend Darkrai and Arceus
Shadow Force Arceus
Endeavor Pichu and Pikachu
Rest Pikachu
Sleep Talk Pikachu, Poliwag, Cleffa, and Barboach
Yawn Farfetch'd, Kangaskhan, Pikachu
Snore Pikachu
Protect Pikachu, Politoed, and Kingdra
Attract Eevee and Miltank
Blaze Kick Genesect
Aromatherapy Snivy
Draco Meteor Jirachi
Octozooka Sableye
Barrier Porygon, Ledyba, and Dragonite
Hypnosis Misdreavus
Low Kick Doduo
Fury Attack Cubone and Dunsparce
Morning Sun Nidoran♂
Toxic Milotic
Meteor Mash Jirachi
Shift Gear Genesect
Hurricane Mewtwo and Lugia
Blue Flare Victini
Bolt Strike Victini
Glaciate Victini
V-Create Rayquaza and Victini
False Swipe Machop, Bulbasaur, Charmander, Squirtle, and Jumpluff
Block Bulbasaur, Charmander, and Squirtle
Frenzy Plant Bulbasaur
Acrobatics Charmander
Blast Burn Charmander and Arceus
Hydro Pump Squirtle and Arceus
Pursuit Elekid
Scary Face Pichu, Cleffa, Igglybuff, Marill, and Wooper
Beat Up Murkrow
High Jump Kick Lucario
Feint Attack Kangaskhan
Foresight Abra
Disable Aromatisse
Haze Horsea and Zekrom
Moonbast Jirachi
Hold Back Mareep, Beldum, Serperior, Emboar, Samurott, and Munchlax
Hold Hands Charizard Pikachu, and Fancy Pattern Vivillion
Substitute Shaymin
Thrash Machop
Celebrate Bulbasaur, Charmander, Squirtle, Pikachu, Magikarp, Eevee, Vaporeon, Jolteon, Flareon, Espeon, Umbreon, Ho-oh, Rayquaza, Leafeon, Glaceon, Sylveon, Alolan Vulpix, Alolan Exeggutor, Snorlax, Shaymin, Victini, Meloetta, and Comfey.
Phantom Force Darkrai
Rock Throw Pinsir, Omanyte, Kabuto, and Aerodactyl
Play Rough Jirachi
Hoppy Hour Pikachu, Meowth, Magikarp, Delibirt, Jirachi, Greninja, Inkay, Munchlax, and Rockruff.
Heart Stamp Pikachu and Jirachi
Disarming Voice Rotom
Sonic Boom Spearow and Scyther
Lovely Kiss Nidoran♀, Nidoran♂, Poliwag, Bellsprout, Snorlax, and Snubbull
Moonlight Nidoran♀ and Sneasel
Tri Attack Psyduck
Growth Poliwag, Eevee, and Spinarak
Rapid Spin Geodude
Sharpen Onix
Sweet Scent Exeggcute, Chansey, and Pikachu
Dizzy Punch Sentret and Marill
This link and this link will take you to Bulbapedia articles that have Gotta catch 'em all! Station events listed. Events titled [Move] [Pokemon] generally mean that that move is (at least, for that generation) an event exclusive move for that Pokemon.
Sources: This and looking at quite a few of Bulbapedia's pages on certain moves.
