What Pokemon can be obtained without using a pokeball in each game?

Question

This includes all gift eggs, gift Pokemon, starters, and any others that for some reason don't require the use of a pokeball. this doesn't include mystery gifts or player trades, however.

Comments

Not a full answer, but https://bulbapedia.bulbagarden.net/wiki/Gift_Pok%C3%A9mon

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Starters of course
If you have Pokemon let's go Pikachu/Eevee records on your switch then at the train station you have to talk to two kids they will give you pikachu if you have let's go pikachu or eevee if you have let's go eevee (you can gigantamax them) they're level 10
on route 5 at day care center you can obtain toxel at level 1
on route 6 there is a lady that will combine your two fossils you can gain: Dracozolt,Arctozolt,Dracovish and Arctovish at level 10
In the post game you can obtain Type:null in the battle tower at level 50
in Postwick in the post game you can obtain an charmander it's in Leon room it's capable of gigantamaxing as a Charizard
that's all

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Moved to a comment, since this only covers Sw/Sh when the question asked for every game.

Answer 1

Gen I
Bulbasaur/Charmander/Squirtle (Starter)
Pikachu (Starter, only in Yellow)
Magikarp (Magikarp Salesman, 500 Pokedollars)
The Hitmons (Karate Master)
Eevee (Celadon Mansion)
Lapras (Silph Co.)

Gen II
Chikorita/Cyndaquil/Totodile (Starter)
Togepi (Egg from Elm's aide)
Pichu, Cleffa, Igglybuff, Tyrogue, Smoochum, Elekid, Magby (Eggs from Day Care man)
Kenya the Spearow (Route 35)
Eevee (Bill, Ecruteak City)
Shuckie the Shuckle (Cianwood City)
Dratini (Dragon's Den)
Tyrogue (Karate Master, Mt. Mortar)

Gen III (R/S/E)
Treecko/Torchic/Mudkip (Starter)
Wynaut (Egg from lady in Lavaridge)
Castform (Weather Institute)
Beldum (Steven in Mossdeep)
Johto Starters (Prof. Birch after you beat the game)

Gen III (FR/LG)
Same as Gen I, but with no Pikachu, and with the addition of Togepi (Gentleman, Water Labyrinth)

Gen IV (D/P/Pt)
Turtwig/Chimchar/Piplup (Starter)
Togepi (Egg, Cynthia, Platinum only)
Eevee (Bebe, Hearthome City)
Happiny (Egg, Hearthome City)
Porygon (Veilstone City)
Riolu (Egg, Riley, Iron Island)

Gen IV (HG/SS)
Same as Gen II, but with Mareep, Wooper, Slugma (Eggs from Primo), Kanto Starters (Oak), and Hoenn Starters (Birch)

Gen V (Black/White)
Snivy/Tepig/Oshawott (Starter)
Pansage, Pansear, Panpour (Depends on your starter)
Zorua (Castelia City, must have Celebi)
Larvesta (Egg, Route 18 rest house)
Previous generation fossils (One offered per day, Twist Mountain)
Magikarp (Magikarp Salesmaqn, Marvelous Bridge)

Gen V (B2/W2)
Same as Black and White, but with Deerling (Weather Institute), Shiny Dratini or Gible (Benga, Floccessy Town) and N's Zorua (Driftveil City)

Gen VI (X/Y)
Chespin/Fennekin/Froakie (Starter)
Kanto Starters (Only one-Prof. Sycamore, Lumiose City)
Lucario (Korrina, Tower of Mastery)
Lapras (Pokemon Breeder, Route 12)

Gen VI (OR/AS)
Same as Gen III (R/S/E) but with: Cosplay Pikachu (Contest Hall), Latias or Latios depending on version (Southern Island), Unova Starters (Prof. Birch), Camerupt (Magma Grunt), and Sharpedo (Aqua Grunt)

Gen VII (S/M)
Rowlet/Litten/Popplio (Starter)
Eevee (Egg from Breeder in Day Care)
Gen IV and V Fossils (Konikoni City)
Aerodactyl (Seafolk Village)
Porygon (Aether House)
Type: Null (Gladion)

Gen VII (US/UM)
Same as S/M, but with all other fossils, Pikachu (Surf Association), Poipole (Ultra Megalopolis), and Zygarde 10% (Dexio, Route 16)

Gen VII (LGP/E)
Same as Gen I, but with Arcanine (Vermilion City) and Persian (Vermilion City)

Gen VIII (SwSh)
Grookey/Scorbunny/Sobble (Starter)
Pikachu (Wild Area Station)
Eevee (Wild Area Station)
Toxel (Breeder, Route 5)
The fossils (Cara Liss, Route 6)
Charmander (Leon's House)
Type: Null (Battle Tower)

Gen VIII (Isle of Armor DLC)
Bulbasaur/Squirtle (From Honey in the Master Dojo)
Kubfu (Mustard in the Master Dojo)
Porygon (Hyde in the Master Dojo)
Alolan Meowth (Hiker, 5 Diglett found)
Kantonian Slowpoke (Hiker, 10 Diglett found)
Alolan Vulpix (Hiker, 20 Diglett found)
Alolan Sandshrew (Hiker, 30 Diglett found)
Alolan Raichu (Hiker, 40 Diglett found)
Alolan Marowak (Hiker, 50 Diglett found)
Alolan Exeggutor (Hiker, 75 Diglett found)
Rowlet (Hiker, 100 Diglett found, Grookey as starter)
Litten (Hiker, 100 Diglett found, Scorbunny as starter)
Popplio (Hiker, 100 Diglett found, Sobble as starter)
Alolan Diglett (Hiker, 150 Diglett found)

Gen VIII (Crown Tundra DLC)
Cosmog (After saving Freezington from Glastrier/Spectrier, you will be offered a Cosmog)
Poipole (After Poipole appears in the Max Lair, the leader of the Dynamax Adventures asks you to take it)

Gen VIII (BD/SP)
Same as Gen IV, with the addition of:
Mew (Floaroma Town, with LGPE save data)
Jirachi (Floaroma Town, with SwSh save data)

Gen VIII (Legends: Arceus)
Rowlet/Cyndaquil/Oshawott (Starter)
Vulpix (From Keaka after finding all five Vulpix during Request 83)
Arceus (After defeating Arceus, it grants the player a part of itself)

Gen IX (SV)
Sprigatito/Fuecoco/Quaxly (Starter)
Meowth (From Salvatore)
Koraidon/Miraidon (Zero Lab)

Gen IX (Teal Mask DLC)
Turtwig/Chimchar/Piplup (Egg from Jacq on Reveler's Road)
Hisuian Growlithe (Mossui Town from Perrin)
Shiny Munchlax (Kitikami Hall after beating Ogre Oustin' on Hard Difficulty)

Gift Pokemon (Bulbapedia)
Gift Pokemon in Sword and Shield (Serebii)

Hope I helped!

Comments

Close enough, I can fill in the gaps, such as fossils