His father was never introduced. The anime suggests that his father was once a Pokémon Trainer who began his journey in Pallet Town, and that he is still living.
An interview with the series' storyboarder confirmed Ash's father is a Trainer on his own journey. According to the same storyboarder, Ash's father may or may not be introduced in the series, depending on its necessity to Ash's further maturity and development as a Trainer.
Ash is an only child, breaking from the tradition of several other main characters, with the exception of Dawn and possibly Tracey, whose siblings are often a foil or focal point in their lives.