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King Zora is the leader of the Zora race.

A Link to the Past
King Zora is king of the river Zoras in A Link to the Past. He is found by the Zora's Waterfall in Zora's Lake. A naturally friendly character with a generous, predictable laugh, he sells Flippers for 500 Rupees a pair. As a bonus, he tells Link that he can use the Whirlpool Waterways to warp from one body of water to another in Hyrule. Link must meet him and purchase Zora's Flippers in order to complete his quest; if Link does not have enough rupees for  the Flippers, the King will kindly encourage him to find more before  returning.

In Ancient Stone Tablets, King Zora returns in week 1 to sell Zora's Flippers, this time for 300 Rupees.

Ocarina of Time
In Ocarina of Time, he sits on his throne at the helm of Zora's Domain, guarding passage to the great Lord Jabu-Jabu, the patron deity of the Zoras. Only when Child Link presents him with a letter from his incarcerated daughter, held from within Lord Jabu Jabu, does he grant Link passage to Lord Jabu Jabu's lair. When Adult Link ventures to Zora's Domain, he finds King Zora and the rest of the region frozen solid: a curse placed on the region that stems  from Morpha's control of the the Water Temple, the source of their water. Freeing King Zora from the ice after completing the Ice Cavern will grant Link a Zora Tunic as a gift. If Link already has a Zora tunic, he will offer him a kiss.

Incidentally, it appears that, according to in-game dialog, King Zora and Biggoron are good friends and have known each other for a long time. During the ending sequence of Ocarina of Time, King Zora is shown to be one of the few characters not celebrating the victory over Ganon, instead sitting next to a grieving Mido.

Oracle of Ages
King Zora also appears in Oracle of Ages in death at the "present time", due to an overwhelming amount of sea  pollution. To save him, Link must travel to the past and give him a life potion. After this, he will grant Link permission to enter Jabu-Jabu if the young hero cleanses the seas, handing over the Library Key as well.

Twilight Princess
The King Zora in Twilight Princess is long dead. He was Queen Rutela's husband and the creator of the Zora Armor. His grave is located in the Kakariko Village Graveyard and is where Link is given the Zora Armor by the ghost of Queen Rutela.

It is implied by Eiji Aonuma that this is the same King Zora as in Ocarina of Time. This is supported by the fact that Queen Rutela states on how her husband created "garments specifically for the chosen hero" that would  allow him to breathe underwater, hinting at the Zora Tunic in Ocarina of Time.

Other Appearances

Majora's Mask Manga
In the, it is suggested that Toto may be the King Zora's Terminan counterpart.

Super Smash Bros. Brawl
The King Zora from Ocarina of Time appears as a sticker in Super Smash Bros. Brawl.

Trivia

 * Wearing the Goron Mask while speaking to King Zora reveals that Biggoron and King Zora are best friends, and have known each other since childhood.
 * The Cutscene in which King Zora moves aside in Ocarina of Time so as to allow Link entry to Jabu Jabu's Lair is possibly one of the most exaggerated cutscenes in the Zelda series, at sixty seconds long.