From the Super Mario Wiki
“Excuse me, everybody! I just closed the peanut butter jar on my tie. Can somebody help me?”
The Mushroom King is a seldom-seen ruler of the Mushroom Kingdom. He is a figure that is absent in the video game series, where the princess is depicted as its current monarch. However, he does make an appearance in other early media.
Super Mario Bros.
In the NES instruction booklet of Super Mario Bros., the Mushroom King is briefly mentioned in passing as the father of Princess Toadstool. With the exception of Super Mario Bros. Deluxe, this is not included in subsequent releases. This is due to the fact that no Japanese manual mentions him, and his hinted existence was invented by the English localization team.
Nintendo Comics System
In the Nintendo Comics System, the Mushroom King is Princess Toadstool's father and the de facto leader of the Mushroom Kingdom. However, he is depicted as scatterbrained and dimwitted, so his responsible daughter often performs his royal duties in his stead. Wooster, one of his subjects, is occasionally at odds with him due to his intelligence.
Based on his role, it is likely that he was based off the Mushroom Kings from Super Mario Bros. 3 as he plays a similar role in the comic strips (having a Magic Scepter that is often taken by Bowser's forces and being transformed into various animals).
Super Mario Bros. Film
King Bowser (not to be confused with the actual President Koopa), as he is known here, appears as a main character in the Super Mario Bros. film. He is Daisy's father and the king of Dinohattan, but had been overthrown and de-evolved by President Koopa into a giant sentient fungus that had spread across the parallel world to obstruct Koopa's construction projects.
He continually aids Mario and Luigi throughout the film in their quest to defeat Koopa. Once they successfully do so by killing Koopa, King Bowser reverts back to his human form and exclaims, "God, I love those plumbers!"
He also appears in the webcomic sequel to the film, although he is renamed Reznor.