Kings of this legend:

Ailill: Ailill was a powerful king in Ireland, largely because he was the husband of Medb. We see early on that although Ailill was well-off before the marriage, union with Medb is what gave him the power he held during the events that take place in the Táin. Medb was the favorite daughter of her father, Eochu Feidlech, who was the "High King of Ireland". Whether this means that Eochu was the Rí Ardrí or simply a Rí Ruriech is unknown. Either way, Eochu amassed enough wealth and prestige to make Medb one of the most powerful people in Ireland, regardless of gender. As a result of their independent successes, Medb and Ailill had an argument about which one of the two of them was more affluent, which they settled by matching up all of their possessions; cow for cow, jewel for jewel, soldier for soldier, etc. This was the very conflict, in fact, which began their campaign against the UIstermen, and set the events of the Táin in motion.
In spite of this seemingly prideful argument, Ailill seems perfectly content to let Medb lead their forces on the campaign. In addition to this seemingly submissive behavior, Medb described Ailill as "without jealousy, meanness, [or] fear". These attributes are reinforced during the rest of the Táin, while Ailill remained neutral to Medb's often diabolical schemes, and did nothing more than steal Fergus' sword when he discovered he was sleeping with his wife. Admittedly, taking a warrior's sword is a severe blow, but remains merciful when compared with taking his life. Ailill clearly demonstrated that he had the rígdomna to be the king, being capable in appearance, bravery, temperance, and wisdom.

Conchobar: Conchobar was the king of Ulster during the events of the Táin. He is the foster father of Cú Chulainn, as well as his maternal uncle by blood. He was the one who gave Cú Chulainn his weapons and his chariot, since noe other equipment could survive the young boy's might. In fact, Conchobar is so tied to the Irish hero that his name means, literally, "hound lover".

Fergus Mac Róich: While Fergus is not a king during the events of the Táin, he was once the king of the Ulstermen. The story goes that Fergus fell in love with Conchobar's mother, who agreed to sleep with him only if he would give the kingship of the Ulstermen to her son for one year. Fergus agrees, but in that year, his mother steals a fortune from one half of her people and gives it to the Ulster warriors. Because of Fergus' disloyalty to them and because of Conchobar's generosity, they decide to retain the boy as their king, and so depose Fergus. In spite of this, Fergus stays in Ulster as a nobleman, and in fact develops a friendship with the boy who deposed him; the Táin references the two of them playing chess when they first encounter Cú Chulainn as a young boy. Fergus is also the foster father of Cú Chulainn, and as such retains a close bond with the warrior, even though they are on opposite sides of the conflict. Because of this bond, Fergus is the advisor to Ailill and more appropriately Medb on all things related to Ulster and particularly Cú Chulainn. He also acts as the intermediary between Cú Chulainn and the Connachtmen, discussing truces and warning Cú Chulainn about challenges he will face.
For the complete version of this epic story please go here.