Outside the Poké Ball
On day one, Pikachu wants nothing to do with Ash: it shocks him, dodges the Poké Ball and only moves when dragged on a rope. Everything changes when a flock of Spearow attacks. Ash shields Pikachu with his own body, and Pikachu, though hurt, unleashes a huge bolt to save him. From then on they're inseparable, and Pikachu rides on his Trainer's shoulder instead of in the ball. It only ever says versions of its own name, "pika" and "pikachu," and everyone still gets what it means.
In episode two, Team Rocket sees its power during a raid on the Viridian City Pokémon Center and decides to steal it. At the Vermilion Gym, Pikachu loses to Lt. Surge's Raichu. Ash offers a Thunder Stone so it can evolve, and Pikachu refuses: it wins the rematch as a Pikachu, using its speed. Later, Ash considers leaving it with a colony of wild Pikachu, and Pikachu chooses to come back to him.