Here's a few:
"The Battle of Champions was a Scottish clan battle fought in 1478 between members of the Clan Gunn and Clan Keith in Caithness, in the Scottish Highlands.
It is recorded that the feud began when Dugald, Chieftain of the Keiths, abducted Helen of Braemore, daughter of Lachlan Gunn, when he discovered the she was betrothed to Alexander Gunn. The attack occurred on the night before the wedding, and Alexander was one of those slain by the Keiths. Helen subsequently committed suicide by throwing herself off Ackergill Tower. Subsequent conflicts between the two clans were for the most part indecisive, and losses were numerous on both sides. After long querelling between the Keiths and Gunns it was decided that a "battle of chmpions" would be fought between twelve men on horseback on either side. However the Keiths arrived with two men on each of their twelve horses"
"The Battle of the 300 Champions was a battle fought in roughly 545 BC between Argos and Sparta. Rather than commit full armies both sides agreed to pitting 300 of their best men against each other. After a bloody battle only three men remained, two Argives and one Spartan. The Argives claimed that because of numerical superiority they had won the battle and returned home. The lone Spartan, however, declared victory for Sparta since he was the last soldier to maintain his proper post on the battlefield and constructed a victory shrine for Sparta. Argos did not take too kindly to this and sent their entire hoplite army which was met by a Spartan force of equal magnitude. The Spartans won a decisive victory and as a result gained control of Thyreatis."
"The Persians, who were one of the first non-Arab people, on whom the Muslims fell upon, had a tradition of single combat, which they used in many battles. The strongest person from each army would fight the champion of the adversary’s army. The winner’s army would be deemed to have won the battle, and the actual battle was not then fought, as both the armies were honor-bound to abide by the result of the duel. The duel was a test of strength and skill. The opponents were not bound to kill their adversary, but only to defeat him, and in most cases the defeated champion was allowed to return to his camp, and his army withdrew thus preventing a battle and saving of many lives. The Persians, the pre-Islamic Turks, the Greeks and Romans had used this practice of single-combat to settle the result of many a battle. This practice was fine as long as both the adversaries were bound by honor. "
Also, the battle between David and Goliath was a battle of champions. This was quite a common way of settling disputes in the days of Saul.