Kingship is the position and power of a king. There have been many kings in the Known World. In Westeros, kings inherit the title when they are the next male in line. Each of the Seven Kingdoms of Westeros had a king once, though Dorne started using the title "Prince of Dorne" after Lord Mors Martell married Queen Nymeria, and the new rulers chose to abandon the Andal customs in favor of those of the Rhoynar.
It is stated that Ghiscar had a king once, but the custom was not renewed until Daenerys Targaryen conquered Slaver's Bay. It is not known if the cities of the east have kings or not. In the Free Cities the ruler is elected through democracy, while in Braavos there are Sealords.