Its first king was Godfrey of Bouillon, and the title passed through different European dynasties, including that of the Hohenstaufens from 1228 until 1268 and the death of young Conradin, the Duke of Swabia.
Conradin inherited the title when he was two years old, though Pope Alexander IV felt he was too young to assume the role. At his death, he had no heirs, having spent his "productive" years in war and getting beheaded at the age of 16.
Conradin's death raised the question of legitimate inheritance of the title. The most appropriate link went back to the descendants of his great-great-grandmother, Isabella I of Jerusalem (1172 - 1205). There were enough descendants that disagreements arose, however. Hugh of Brienne was the technical heir due to the laws of primogeniture. Hugh III of Cyprus, however, had actually been managing the kingdom as regent for Conradin and made a sensible claim that he was the appropriate next King of Jerusalem. A third candidate, Maria of Antioch, said that she was the closest blood relation to Conradin (as his grandmother's first cousin) and had the right to the title. She received nominal support from the Knights Templar (unusual choice, but there is speculation that the Knights wanted her to be a weak ruler so they could manage more of the territory), but everyone else rejected her claim; she moved to Europe and "sold" her claim to none other than Charles of Anjou, the man who beheaded Conradin!
Hugh of Brienne and Hugh of Cyprus were cousins, and had been raised together, but their competing goals to be named King of Jerusalem damaged their relationship. The High Court of Jerusalem noted that their relationship to Conradin had been genealogically identical; the decision was to choose the elder of the two, and that was Hugh of Cyprus, who was about five years older (born about 1235). The Kingdom of Jerusalem was now in the hands of the Lusignan dynasty, who managed it until its final dissolution in 1291 with the fall of its capital, Acre, to the Mamluks.
While writing this post, I have discovered that in 1,111 posts since May of 2012, I have never mentioned "primogeniture" before or explained it. I will correct that omission on the morrow.