Special Pokemon

Tree (Use Headbutt)
Gold Version (Wooded Areas): Caterpie, Metapod, Butterfree, Exeggcute, Pineco.
Gold Version (Mountain Areas): Spearow, Heracross, Aipom.
Silver Version (Wooded Areas): Weedle, Kakuna, Beedrill, Exeggute, Pineco.
Silver Version (Mountain Areas): Spearow, Heracross, Aipom.

Important Trainer Numbers
Fisherman: Ralph at Route 32, informs you of Qwilfish in the area.
Hiker: Anthony at Toute 33, informs you of Dunsparce in the area.
Bug Catcher: Arnie at Route 35, informs you of Yanma in the area.
Schoolboy: Chad at Route 38, informs you of Snubbull in the area.
Fisherman: Wilton at Route 44, informs you of Remoraid in the area.
Hiker: Parry at Route 45, informs you of Marrill in the area.

Trade Evolutions
Kadabra ---> Alakazam
Graveler ---> Golem
Haunter ---> Gengar
Machoke ---> Machamp

Trade Evolutions With Held Items
Poliwhirl w/ King's Rock ---> Politoed
Slowpoke w/ King's Rock ---> Slowking
Onix w/ Metal Coat ---> Steelix
Scyther w/ Metal Coat ---> Scizor
Seadra w/ Dragon Scale ---> Kingdra
Porygon w/ Upgrade ---> Porygon2

Stone Evolutions
---Water Stone:
Poliwhirl ---> Poliwrath
Shellder ---> Cloyster
Staryu ---> Starmie
Eevee ---> Vaporeon
---Fire Stone:
Vulpix ---> Ninetales
Growlithe ---> Arcanine
Eevee ---> Flareon
---Leaf Stone:
Weepinbel ---> Victreebel
Exeggute ---> Exeggutor
Gloom ---> Vileplume
---Thunder Stone:
Pikachu ---> Raichu
Eevee ---> Jolteon
---Moon Stone:
Nidorina ---> Nidoqueen
Nidorino ---> Nidoking
Clefairy ---> Clefable
Jigglypuff ---> Wigglytuff
---Sun Stone:
Sunkern ---> Sunflora
Gloom ---> Bellossom

Happiness Evolutions
Pichu ---> Pikachu
Togepi ---> Togetic
Cleffa ---> Clefairy
Chansey ---> Blissey
Igglybuff ---> Jigglypuff
Golbat ---> Crobat
Eevee ---> Espeon (day) or Umbreon (night)
 

Gift Pokemon
Chikorita, Cyndaquil, Totodile: New Bark Town, Professor Elm gives you one of them.
Shuckle: Cianwood City, a guy inside a building will give you it.
Eevee: Goldenrod City, after you meet Bill, go to his house and get an Eevee.
Tyrogue: Mt. Mortar, defeat Blackbelt Kyo to get Tyrogue.

Game Prizes
---Goldenrod City:
Abra: 200 Coins
Ekans (Gold version): 700 Coins
Sandshrew (Silver version): 700 Coins
Dratini: 2,100 Coins
---Celadon City:
Mr. Mime: 3,333 Coins
Eevee: 6,666 Coins
Porygon: 9,999 Coins

In Game Trades
Violet City: Bellsprout ---> Onix
Goldenrod City: Drowzee ---> Machop
Olivine City: Krabby ---> Voltorb
Blackthorn City: Dragonair (female) ---> Rhydon
Pewter City: Gloom ---> Rapidash
Route 14: Chansey ---> Aerodectyl

National Park: Bug Catching Event
Caterpie, Metapod, Butterfree, Weedle, Kakuna, Beedrill, Venonat, Paras, Scyther, Pinsir.

No Eggs (Can't produce eggs)
Unown, Igglybuff, Togepi, Cleffa, Tyrogue, Smoochum, Elekid, Magby, Articuno, Zapdos, Moltres, Mewtwo, Mew, Raikou, Entei, Suicune, Nidorina, Nidoqueen, Pichu, Lugia, Ho-oh.

Always Female Pokemon
Nidoran (female), Nidorina, Nidoqueen, Jynx, Smoochum, Kangaskhan, Miltank, Chansey, Blissey.

Always Male Pokemon
Nidoran (male), Nidorino, Nidoking, Hitmonlee, Hitmonchan, Hitmontop, Tyrogue, Tauros.

Always No Gender Pokemon
Magnemite, Megneton, Ditto, Voltorb, Electrode, Staryu, Starmie.

Unavailable in Gold Version
Vulpix, Ninetales, Meowth, Persion, Phanpy, Donphan, Skarmory, Ledyba, Ledian, Delibird.

Unavailable in Silver Version
Mankey, Primeape, Growlithe, Arcanine, Teddiursa, Ursaring, Gligar, Spinarak, Ariados, Matine.

Unavailable in Gold and Silver Versions
Bulbasaur, Ivysaur, Venusaur, Squirtle, Wartortle, Blastoise, Charmander, Charmeleon, Charizard, Articuno, Zapdos, Moltres, Kabuto, Kabutops, Omanyte, Omastar, Mewtwo.

Mew and Celebi
These two Pokemon can't be captured in Gold/Silver. However, you can get during a Nintendo promotion such as a Pokemon Mall Tour.