The character of Dad from EarthBound is Ness's unseen father, who appears only as a voice in the telephone. Ness's dad works faraway from Eagleland, which means he can't see his son or daughter regularly. He thinks his children like to work hard, just like their mother, but he doesn't think it's good to work too hard, much like Ninten's dad. In order to save the game, it is necessary to call dad. He also deposits money into Ness's account as he progresses through his adventure, and will even pay his son's debts by the end of the game. After Giygas is defeated, he states he'll be present at Onett for Ness's fourteenth birthday. It is stated in the EarthBound's Playing Guide that Ness's father works at the hamburger industry.
The Minch family appears to hold a grudge against Ness's father because Aloysius Minch loaned him a few hundred thousand dollars, or maybe a lot less but he doesn't remember correctly, and was never repaid.
At the end of the game, the pictures of all major characters appear. As Ness's dad is never seen, he is replaced by a telephone. This happens in Mother 1+2 commercials as well.