Technically, every Generation 1 Pokemon species exists in every game, but sometimes you need to trade in order to get a Pokemon of a certain species. These are the ones you never need to trade for.
Jigglypuff, Wigglytuff, Zubat, Golbat, Horsea, Seadra, Goldeen, Seaking, Magikarp, Gyarados
Psyduck and Golduck are in every game except LeafGreen.
Abra, Kadabra, and Alakazam are in every game except White.
Magnemite and Magneton are in every game except Black.
Rhyhorn and Rhydon are in every game except Black.