Every Pokemon here fits into one of these four categories unless otherwise specified: Legendary Pokemon, Gift Pokemon, Interactable Pokemon and In-Game Trades. Comment below if there's anything mistakes because there probably will be some...
Gen I
Red and Blue
- Legendary Pokemon
- Bulbasaur, Charmander and Squirtle
- Snorlax
- Hitmonlee/Hitmonchan
- Lapras
- Eevee
- Omastar/Kabuto
- Aerodactyl
- Mr. Mime
- Farfetch'd
- Jynx (freely available in Jp. Red & Green
Yellow
- Starter Pikachu (available in Red, Blue & Green though)
- Virtually every Pokemon listed above.
Gen II
Gold and Silver
- Legendary Pokemon
- Chikorita, Cyndaquil, Totodile
- Togepi
- Shuckle
- Snorlax
- Sudowoodo
- Aerodactyl
Crystal
- Celebi (event)
- The Pokemon listed above.
Gen III
Ruby & Sapphire
Emerald
FireRed & LeafGreen
- Legendary Pokemon
- Bulbasaur, Charmander, Squirtle
- Snorlax
- Hitmonlee and Hitmonchan
- Lapras
- Eevee
- Omantye and Kabuto
- Aerodactyl
- Togepi
- Lickitung
- Farfetch'd
- Jynx
Words of wisdom: breeding was introduced in Gen II and global trading was introduced in Gen IV, so all of these Pokemon are far from having a limited availability. This is just 'limited availability' in that you're too lazy to breed them, you're internet connection sucks and you don't have any friends. Don't worry, I am all of those things.
I plan to finish this later but just letting everyone know that I can answer this; Indi has got things under control.
Hope I helped. :)
Source: Basically every Serebii page in existence
