Since there are already rumors of datamines, here's a list of all the suggestions we've made in this thread so far:
Venusaur: Flower Shield.
Squirlte/Wartortle/Blastoise: Snipe Shot. Wave Crash, Zap Cannon.
Beedrill: Cross Poison.
Fearow: Slash.
Pikachu/Raichu: Knock Off.
Sandslash: Dire Claw
Igglybluff/Jigglypuff/Wigglytuff: Sweet Scent.
Parasect: Poison Jab.
Primeape: Lash Out.
Poliwrath: Flip Turn.
Bellsprout/Weepinbell/Victreebel: Heal Bell
Tentacool, Tentacruel: Power Gem.
Golem: Shell Smash. Steel Roller.
Slowpoke/Slowbro/Slowking: Shed Tail.
Dewgong: Aurora Veil, Calm Mind, Hydro Pump, Iron Head,Recover.
Onix/Steelix: Body Press (Only Learn In Sw/Sh) Coil.Glare.
Cubone, Marowak, AlolanMarowak: Victory Dance,
Kantonian Marowak: HeadSmash, Ice Punch.
Alolan Marowak: Phantom Force.
Horsea/Seadra/Kingdra: Snipe Shot.
Scyther, Scizor, Kleavor: Bug Bite. Fly. Victory Dance
Pinsir: Mega Horn.
Gyarados: Fly. Wave Crash.
Lapras: Shell Smash
Eevee: Veevee Volley. (Only LetsGo Move)
Vaporeon: Bouncy Bubble.
Jolteon: Buzzy Buzz.
Flareon: Sizzly Slide.
Aerodactyl: Brave Bird, Head Smash.
Chikorita/Bayleef/Meganium: Cotton Guard
Totodile/Croconaw/Feraligatr: Wave Crash.
Ledian: Cosmic Power, Foul Play, Iron Defense, Seismic Toss.
Xatu: Esper Wing
Soodowoodo: Iron Head
Politoed: Extrasensory
Espeon: Glitzy Glow. Power Gem,
Umbreon: Baddy Bad.
Galarian Slowking: Mystical Fire.
Forretress: Body Press. Shell Smash,
Dunsparce: Fire Fang, Ice Fang, Thunder Fang.
Heracross: Drain Punch. Posion Jab. X-Scizzor.
Sneasel/Weavile: Mountain Gale. Knock Off.
Teddiursa/Ursaring/Ursaluna: Cosmic Power
Remoraid/Octillery: Octolock. Snipe Shot,
Phanphy/Donphan: Watergun. (Egg Move Only in Gen 2). Steel Roller.
Lugia: Esper Wing. Silver Wind.
Treecko/Grovyle/Sceptile: Shed Tail
Blaziken. Pyro Ball.
Migthyena: Psychic Fangs.
Linoone: Wild Charge.
Swellow: Dual Wingbeat, Esper Wing.
Shedinja: Shell Smash
Sableye: Phantom Force
Mawile: Jaw Lock.
Sharpedo: Fishious Rend. Jaw Lock.
Spinda: Superpower
Zangooze: Agility. Cross Poison. Cut. Dire Claw.
Banette: Bitter Malice
Dusclops/Dusknoir: Phantom Force
Snorunt/Glalie: Mega Horn. Mountain Gale.
Relicanth: Iron Head.
Salamence: Iron Head.
Regirock: Rock Wrecker.
Regice: Body Press.
Infernape: Pyro Ball.
Staraptor: Dual Wingbeat, Lash Out, Payback. Revenge, Smart Strike, Slash.
Bastiodon: Body Press, Foul Play, Night Shade, Recover, Wish.
Pachirisu: Stuff Cheeks.
Gastrodon: Gastro Acid.
Mismagius: Eerie Spell.
Skuntank. Dire Claw.
Garchomp: Acrobatics. Air Slash. Dragon Dance. Dual Wingbeat. Fly. Sky Attack. Steel Wing.
Carnivine: Snap Trap.
Snover/Abomasnow: Mountain Gale.
Electivire: Bulk Up.
Yanmega: Fly.
Leafeon: Sappy Seed.
Glaceon: Freezy Frost. Mountain Gale, Surf.
Gliscor: Crunch. Dire Claw. FLy.
Froslass: Mountain Gale. Perish Song,
Uxie: Blizzard. Power Gem.
Mexpist, Azelf: Power Gem.
Heatran: Scald.
Victini: Victory Dance
Serperior: Superpower
Emboar: Close Combat. Coaching.
Samurott: Shell Smash.
Stoutland: Double-Edge.
Musharna: Strange Steam.
Tranquill/Unfezant: Close Combat. Double-Edge. Double-Kick, Lash Out, Peck, Nasty Plot, Play Rough, Slash, Smart Strike, Wing Attack.
Zebstrika: High Horsepower, Lash Out, Rising Voltage, Thunder Cage, Triple Axel.
Swoobat: Esper Wing
Sandile/Krokorok/Krookodile: Fake Tears. Jaw Lock.
Escavalier: Gyro Ball.
Hisuian Zoroark: Phantom Force
Swanna: Aqua Jet, Calm Mind, Dual Wingbeat, Esper Wing, Life Dew, Payback, Smart Strike,
Axew/Fraxure/Haxorus: Stone Axe.
Galarian Stunfisk: Gyro Ball. Play Rough. Psychic Fangs. Seed Bomb. Wild Charge.
Druddigon: Dire Claw.
Pawniard, Bisharp: Stone Axe.
Kyurem: Mountain Gale.
Chespin/Quilladin/Chesnaught: Drum Beating.
Delphox: Eerie Spell
Gogoat: Grassy Glide, Head Smash, Rock Wrecker.
Aegislash: Phantom Force
Swirlix, Slurpuff: Lick.
Dragalge: Petal Dance.
Heliolisk: Tri-Attack.
Aurorus: Power Gem.
Sylveon: Sparkly Swirl.
Dedenne: Recycle.
Noivern: Dragon Tail.
Dartrix, Decidueye: Curse.
Litten, Torracat, Incineroar: Dig.
Toucannon: Bolt Beak.Dual Wingbeat,
Gumshoos: Trump Card.
Crabominable: Ice Shard, Mach Punch. Mountian Gale,
Oricorio: Nasty Plot.
Lycanroc: Dig. Dire Claw
Wishiwashi: Wish.
Mareanie/Toxapex: Barb Barrage
Comfey: decorate.
Golisopod: Wave Crash
Minior: Meteor Beam.
Komala: Drum Beating.
Turtonator: Fire Punch.
Komoo-o: Victory Dance
Nihilego: Hypnosis, Mind Reader.
Magearna: Power Gem.
Scorbunny/Raboot: Pyro Ball.
Inteleon: Camouflage, Lock-On.
Greedent: Recycle
Dubwool: Explosion.
Applin: Apple Acid/Grav Apple.
Obstagoon: Wild Charge.
Sirfetchd: Slash
Frosmoth: Mountian Gale.
Stonjourner: Blaze Kick.
Zamazenta: Body Press.
Kubfu, Urshifu: Victory Dance.
Kleavor: Accelerock. Bulldoze. Cross Poison. Crunch. Iron Defense. Iron Head. Low Sweep. Lunge. Recover. RockPolish. Roost. Skitter Smack.
Basculegion: Hydro Pump. Phantom Force. Poltergeist.
Enamorus: Fly.
Sprigatito: Energy Ball.
Fuecoco: Fire Fang. Fire Punch. Flamethrower. Slash.
Quaxly: Surf.
Klawf: Baton Pass.
Armarouge: Aura Sphere. Flamethrower. FlashCannon. ShadowBall. Zap Cannon.
Ceruledge: Leaf Blade. Night Slash. Psycho Cut. Slash.
Cetitan: Body Press. Brine. Earthquake. Horn Drill. Ice Hammer. Icicle Crash. Icicle Spear. Water Spout.
Koraidon: Agility. Flame Wheel. Gear Grind. Gear Up. Psycho Shift.