From Bulbapedia, the community-driven Pokémon encyclopedia.
A Pokémon's base friendship is the value to which its friendship is set when the Pokémon is caught, received from an event or NPC, or received from a trade with another player. If a Pokémon is caught in a Friend Ball, however, it will always start out with 200 friendship. If a Pokémon hatched from an Egg, it will start with 120 friendship.
In Generation III, different species of Pokémon were given the ability to have different base friendship values.
In Pokémon Yellow, Red's Pikachu has a base friendship of 90.
In Generation II, all Pokémon have a base friendship of 70.
Generation III onward
In Pokémon Black 2 and White 2, N's Pokémon start with maximum friendship.
Starting in Generation VI, if a Pokémon is traded back to its Original Trainer, it will remember the friendship it had with that Trainer before being traded away.