A king was a male monarch, the hereditary ruler of a kingdom.
Leonidas was a Spartan king who led his people in the Battle of Thermopylae. (DS9: "What You Leave Behind")
King Arthur was a mythical English king. (DS9: "The Muse")
Hamlet was a 7th century Danish king, whose murder was avenged by his son. (TOS: "The Conscience of the King")
Macbeth was a 11th century Scottish king. He gained the throne by murdering King Duncan. (TOS: "The Conscience of the King")
Brian Boru was the High King of Ireland in the 11th century. The King of Leinster was also a King in Ireland. (DS9: "Bar Association")
Henry V was a 15th century English king, a campaigner in France. (TNG: "The Defector")
Henry VIII was a 16th century king in England. (TNG: "In Theory")
In 2266 (stardate 2817.2) the Koridian Company performed Shakespeare's Macbeth on Planet Q and Hamlet aboard the USS Enterprise. (TOS: "The Conscience of the King")
The title of this TOS episode comes from the play Hamlet, Act II, Scene 2.
In 2366 Data performed a scene from Shakespeare's Henry V on the holodeck. (TNG: "The Defector")
The King was a fictional character in the Earth fairy tale Rumpelstiltskin. (DS9: "If Wishes Were Horses")
Quark was known as "The Synthehol King" on Ferenginar. (DS9: "Body Parts")
The Doctor once encountered King Hrothgar in a holonovel. (VOY: "Heroes and Demons")
In 2374, Jack, Lauren and Patrick compared Dukat to a king who lost his throne. (DS9: "Statistical Probabilities")
After exposing the Balancar Agricultural Consortium squill stockpiling, Quark called himself "the king of squill". (DS9: "The Magnificent Ferengi")