Two kings appear in The Minish Cap. King Daltus is the current ruler and Zelda's father. He was a fine swordsman in his youth, and fought his good friend Smith to a draw in one instance of the Picori Festival.
The other one is King Gustaf, an old king who appears as a ghost in the Royal Valley. He was quite fond of the Wind Tribe.
The Legend of Zelda (cartoon)
The King of Hyrule is named King Harkanian in the cartoon shown Fridays on The Super Mario Bros. Super Show! In the cartoon, he is shown to be somewhat absent minded.