Baseball is a popular sport in the Pokémon World. It is usually represented through episodes of the Pokémon anime that feature Casey, a big fan of baseball.

Three episodes have featured baseball as a major theme:

The introduction of Casey in The Double Trouble Header contained many baseball references. Team Rocket had a baseball themed motto and the final confrontation took place on a baseball pitch.
In A Date with Delcatty, Georgio wanted to go on a date with Misty to the Starmie-Electabuzz game.
Casey managed to help her team in Those Darn Electabuzz by helping their star pitcher to regain his confidence.

Other episodes with Casey have had a more minor mention of baseball, usually through her singing the Electabuzz song.

Teams

To include the spirit of Pokémon, the teams are all named after a particular species:

The Electabuzz: Casey's favourite team. Their star pitcher is Corey DeMario.
The Starmies: The biggest rival of the Electabuzz. Their stadium is in Cerulean City.

Trivia

The inclusion of baseball in Pokémon, where the focus is on Pokémon battles, is likely due to its high popularity in Japan. During the baseball season, it is common for weeks to be skipped over due to TV Tokyo giving the sport priority over the show.