Keep in mind that this answer in currently incomplete.
This answer will be for Generation 7. Also, currently, I'll only be including level up moves.
Bulbasaur learns Vine Whip on levels 7 and 9. (S/M only)
Ivysaur learns Leech Seed on levels 1 and 7 and Growl on levels 1 and 3.
Venusaur learns Petal Dance on level 1 and the level it evolves, Vine Whip on levels 1 and 9, Leech Seed on levels 1 and 7, and Growl on levels 1 and 3.
Charmeleon learns Ember on levels 1 and 7.
Charizard learns Wing Attack on level 1 and the level it evolves, Ember on levels 1 and 7, and Flare Blitz on levels 1 and 77.
Wartortle learns Water Gun on levels 1 and 7 and Tail Whip on levels 1 and 4.
Blastoise learns Tail Whip on levels 1 and and Water Gun on levels 1 and 7.
Metapod learns Harden on level 1 and the level it evolves.
Butterfree learns Gust on level 1 and the level it evolves and Confusion on levels 1 and 11.
Kakuna learns Harden on level 1 and the level it evolves.
Beedrill learns Twineedle on level 1 and the level it evolves and Fury Attack on levels 1 and 11.
Pidgeotto learns Sand Attack on levels 1 and 11 and Gust on levels 1 and 9.
Pidgeot learns Sand Attack on levels 1 and 11, Gust on levels 1 and 9 and Quick attack on levels 1 and 13.
Raticate learns Quick Attack on levels 1 and 4 and Focus Energy on levels 1 and 7.
Fearow learns Leer on levels 1 and 4, Pursuit on levels 1 and 8, and Drill Run on levels 1 and 45.
Arkbok learns Crunch on level 1 and the level it evolves, Bite on levels 1 and 9, and Poison Sting on levels 1 and 4.
Sandslash learns Slash on level 1 and the level it evolves, Sand Attack on levels 1 and 3 and Poison Sting on levels 1 and 5.
Nidoqueen learns Superpower on levels 1 and 58.
Nidoking learns Megahorn on levels 1 and 58.
Golbat learns Supersonic on levels 1 and 5, Astonish on levels 1 and 7, and Bite on levels 1 and 11.
Gloom learns Acid on levels 1 and 9 and Sweet Scent on levels 1 and 5.
Parasect learns Absorb on levels 1 and 11 and Poison Powder and Stun Spore on levels 1 and 6.
Venomoth learns Gust on level 1 and the level it evolves, Quiver Dance on levels 1 and 63, Supersonic on levels 1 and 5, and Bug Buzz on levels 1 and 59.
Dugtrio learns Sand Tomb on level 1 and the level it evolves and Growl on levels 1 and 4. (I also learned that Diglett can learn Slash, so have this)
Persian learns Swift on level 1 and the level it evolves, Bite on levels 1 and 6 and Fake Out on levels 1 and 9.
Golduck learns Water Gun on levels 1 and 7 and Tail Whip on levels 1 and 4.
Primeape learns Rage on level 1 and the level it evolves and Final Gambit on levels 1 and 57.
Polywhirl learns Hypnosis on levels 1 and 8 and Water Gun on levels 1 and 5.
Poliwrath learns Submission on level 1 and the level it evolves and Circle Throw on levels 1 and 53.
Kadabra learns Kinesis on level 1 and the level it evolves and Confusion on levels 1 and 16.
Alakazam learns Kinesis on level 1 and the level it evolves and Confusion on levels 1 and 16.
Machoke learns Focus Energy on levels 1 and 3 and Karate Chop on levels 1 and 7.
Machamp learns Strength on level 1 and the level it evolves, Karate Chop on levels 1 and 7, and Focus Energy on levels 1 and 3.
Weepinbell learns Growth on levels 1 and 7 and Wrap on levels 1 and 11.
Victreebel learns Leaf Tornado on level 1 and the level it evolves.
Tentacruel learns Supersonic on levels 1, 4 and Constrict on levels 1 and 7, Wring Out on levels 1 and 56, and Acid on levels 1 and 11.
Graveler learns Rock Polish on levels 1 and 6 and Mud Sport on levels 1 and 4.
Golem learns Heavy Slam on levels 1 and 60, Rock Polish on levels 1 and 6, and Mud Sport on levels 1 and 4.
Rapidash learns Fury Attack on level 1 and the level it evolves, Tail Whip on levels 1 and 4, and Ember on levels 1 and 9.
Slowbro learns Withdraw on level 1 and the level it evolves, Growl on levels 1 and 5, and Heal Pulse on levels 1 and 68.
Magneton learns Thunder Wave on levels 1 and 7 (USUM only), Thunder Shock on levels 1 and 5, Tri Attack on level 1 and the level it evolves .
Dodrio learns Tri Attack on level 1 and the level it evolves , Quick Attack on levels 1 and 5, and Rage on levels 1 and 8.
Dewgong learns Signal Beam on levels 1 and 7, Growl on levels 1 and 3, Icy Wind on levels 1 and 11, and Sheer Cold on level 1 and the level it evolves .
Muk learns Harden on levels 1 and 4, Mud Slap on levels 1 and 7, and Venom Drench on level 1 and the level it evolves.
Haunter and Gengar learn Shadow Punch on level 1 and the level it evolves and Spite on levels 1 and 5.
Hypno learns Confusion on levels 1 and 9 and Disable on levels 1 and 5.
Kingler learns Leer on levels 1 and 9 and Vice Grip on levels 1 and 5.
Electrode Learns Eerie Impulse on levels 1 and 6 and Sonic Boom on levels 1 and 4.
Exeggutor learns Stomp on level 1 and the level it evolves.
Marowak learns Tail Whop on levels 1 and 3, Bone Club on levels 1 and 7, and Headbutt on levels 1 and 11.
Hitmonlee learns Double Kick on level 1 and the level it evolves, Jump Kick on levels 1 and 13, Rolling Kick on levels 1 and 9, Reversal on levels 1 and 61, Close Combat on levels 1 and 57, Mega Kick on levels 1 and 53, and Meditate on levels 1 and 5.
Hitmonchan learns Comet Punch on level 1 and the level it evolves, Close Combat on levels 1 and 66, Counter on levels 1 and 61, Focus Punch on levels 1 and 56, Pursuit on levels 1 and 11, Agility on levels 1 and 6, and Mach Punch on levels 1 and 16.
Weezing learns Double Hit on level 1 and the level it evolves, Smokescreen on levels 1 and 7, and Smog on levels 1 and 4.
Rhyhorn learns Fury Attack on levels 1 and 4 and Scary Face on levels 1 and 9.
Rhydon learns Hammer Arm on level 1 and the level it evolves, Horn Drill on levels 1 and 62, Fury Attack on levels 1 and 5, and Scary Face on levels 1 and 9.
Chansey learns Double-Edge on levels 1 and 54 (S/M) or 65 (USUM).
Seadra learns Smokescreen on levels 1 and 5, Water Gun on levels 1 and 13, Leer on levels 1 and 9, and Hydro Pump on levels 1 and 60.
Seaking learns Megahorn on levels 1 and 54 and Supersonic on levels 1 and 5.
Jynx learns Powder Snow on levels 1 and 11, Lovely Kiss on levels 1 and 8, Lick on levels 1 and 5, and Perish Song on levels 1 and 55.
Electabuzz learns Thunder Shock on levels 1 and 5.
Magmar learns Ember on levels 1 and 5.
Gyarados learns Bite on level 1 and the level it evolves.
Flareon learns Ember on level 1 and the level it evolves.
Jolteon learns Thunder Shock on level 1 and the level it evolves.
Vaporeon learns Water Gun on level 1 and the level it evolves.
Omastar learns Spike Cannon on level 1 and the level it evolves, Bite on levels 1 and 7, and Hyrdo Pump on levels 1 and 75.
Kabutops learns Slash on level 1 and the level it evolves, Absorb on levels 1 and 6, and Night Slash on levels 1 and 72.
Aerodactyl learns Iron Head on levels 1 and 57.
Dragonair learns Twister on levels 1 and 11 and Thunder Wave on levels 1 and 5.
Dragonite learns Hurricane on levels 1 and 81, Wing Attack on level 1 and the level it evolves, Thunder Wave on levels 1 and 5, and Twister on levels 1 and 11.
Bayleef learns Razor Leaf on levels 1 and 6 and Poison Powder on levels 1 and 9.
Meganium learns Petal Dance on the level it evolves and level 1, Petal Blizzard on levels 1 and 70 Razor Leaf on levels 1 and 6, and Poison Powder on levels 1 and 9.
Quilava learns Smokescreen on levels 1 and 6.
Typhlosion learns Smokescreen on levels 1 and 6, Eruption on levels 1 and 82, Double Edge on levels 1 and 74, and Ember on levels 1 and 10.
Croconaw learns Water Gun on levels 1 and 6.
Feraligatr learns Water Gun on levels 1 and 6 and Rage on levels 1 and 8.
Furret learns Agility on the level it evolves and level 1 and Defense Curl on levels 1 and 4.
Noctowl learns Hypnosis on levels 1 and 4 and Dream Eater on levels 1 and 55.
Ledian learns Supersonic on levels 1 and 5 and Swift on levels 1 and 8.
Ariados learns Swords Dance on level 1 and the level it evolves and Absorb on levels 1 and 5.
Crobat learns Cross Poison on level 1 and the level it evolves, Astonish on levels 1 and 7, Bite on levels 1 and 11, and Supersonic on levels 1 and 5.
Lanturn learns Stockpile, Swallow, and Spit Up on level 1 and the level it evolves, Electro Ball on levels 1 and 9, and Thunder Wave on levels 1 and 6.
Togetic learns Sweet Kiss on levels 1 and 9 and Metronome on levels 1 and 5.
Xatu learns Air Slash on level 1 and the level it evolves, Night Shade on levels 1 and 6, and Teleport on levels 1 and 9.
Flaaffy learns Thunder Shock on levels 1 and 8 and Thunder Wave on levels 1 and 4.
Ampharos learns Thunder Punch on level 1 and the level it evolves, Thunder Shock on levels 1 and 8, Thunder Wave on levels 1 and 4, and Dragon Pulse on levels 1 and 65.
Bellossom learns Magical Leaf on level 1 and the level it evolves on and Leaf Storm on levels 1 and 69.
Azumarill learns Tail Whip on levels 1 and 2 and Water Sport on levels 1 and 5.
Sudowoodo learns Slam on the level it evolves and level 1, Flail on levels 1 and 5, Low Kick on levels 1 and 8, and Rock Throw on levels 1 and 12.
Skiploom learns Tail Whip on levels 1 and 6, Synethesis on levels 1 and 4, and Tackle on levels 1 and 8. (S/M
only)
Jumpluff learns Tail Whip on levels 1 and 6, Synethesis on levels 1 and 4, and Tackle on levels 1 and 8. (S/M
only)
Quagsire learns Mud Sport on levels 1 and 5.
Espeon learns Confusion on level 1 and the level it evolves.
Umbreon learns Pursuit on level 1 and the level it evolves.
Slowking learns Heal Pulse on levels 1 and 58.
Forretress learns Mirror Shot and Automize on level 1 and the level it evolves, Heavy Slam on levels 1 and 64, Bug Bite on levels 1 and 9, Zap Cannon on levels 1 and 60, Magnet Rise on levels 1 and 56, and Self-Destruct on levels 1 and 6.
Granbull learns Outrage on levels 1 and 67.
Qwilfish learns Fell Stinger on levels 1 and 60, Destiny Bond on levels 1 and 53, and Hydro Pump on levels 1 and 57.
Scizor learns Feint on levels 1 and 61.
Shuckle learns Sticky Web on levels 1 and 53.
Ursaring learns Hammer Arm on levels 1 and 67.
Magcargo learns Shell Smash on level 1 and the level it evolves , Rock Throw on levels 1 and 8, Ember on levels 1 and 6, and Earth Power on levels 1 and 58.
Piloswine learns Fury Attack on the level it evolves and level 1, Mud Sport on levels 1 and 5, and Powder Snow on levels 1 and 8.
Octillery learns Octazooka on level 1 and the level it evolves, Constrict on levels 1 and 6, Psybeam on levels 1 and 10, and Aurora Beam on levels 1 and 14.
Mantine learns Super Sonic on levels 1 and 3 and Bubble Beam on levels 1 and 7.
Houndoom learns Inferno on levels 1 and 65, Smog on levels 1 and 8, Howl on levels 1 and 4, and Nasty Plot on levels 1 and 60.
Kingdra learns Hydro Pump on levels 1 and 60, Smokscreen on levels 1 and 5, and Leer on levels 1 and 9.
Donphan learns Fury Attack on level 1 and the level it evolves.
Porygon2 learns Zap Cannon on levels 1 and 62 and Magic Coat on levels 1 and 56.
Stantler learns Me First on levels 1 and 55.
Smeargle learns Sketch on levels 1, 11, 21, 31, 41, 51, 61, 71, 81, and 91.
Hitmontop learns Rolling Kick on level 1 and the level it evolves on, Endeavor on levels 1 and 60, Close Combat on levels 1 and 55, Focus Energy on levels 1 and 6, Pursuit on levels 1 and 10, Detect on levels 1 and 50, and Quick Attack on levels 1 and 15.
Blissey learns Double-Edge on levels 1 and 54 (S/M) or 65 (US/UM).
Raikou learns Extrasensory on levels 1 and 64 and Discharge on levels 1 and 57.
Entei learns Eruption on levels 1 and 85, Extrasensory on levels 1 and 64, and Lava Plume on levels 1 and 57.
Suicune learns Bubble Beam on levels 1 and 8 and Rain Dance on levels 1 and 15.
Pupitar learns Sandstorm on levels 1 and 5 and Screech on levels 1 and 10.
Tyranitar learns Sandstorm on levels 1 and 5 and Screech on levels 1 and 10.
Gen 3 can be found here
