Judicial duels in Russia known for a long time. According said the Arab writers, X century Amin Razi and Mukaddezi depicting tradition Russes, "when the king decides to dispute between two litigants, and they remain unhappy with his decision, then he says to them sort it out with their swords - whose sharp, that and win." The Slavs duel was called "field".

The first mention of the field in the Russian sources refer to XI-XII century. According to one version of the chronicle evidence of war sometimes, resolved single combat of two elected from different parties. The competition is going to mean both enemy armies. Outcome it was taken to be an immutable verdict of the divine will, which is equal to obeyed and those on whose share remained victory, and those that had to has pleaded convicted.

I'm not a historian by any means, but there is an example from Livy that I read while studying Latin about a battle between Rome and Alba Longa where this occurred. According to Livy, the Horatii (Rome) and the Curiatii (Alba Longa) were sent forth, each a set of triplets, to battle each other to decide the outcome of the battle. There might be a classicist here that can give you some better background, but here's a link to a translation of Livy. I hope that's helpful!

http://www.perseus.tufts.edu/hopper/text?doc=Liv.%201.24&lang=original

I believe in Ancient Greece, Sparta and Argos were at war and instead of going to a full blown war they each sent 100 champions to fight it out and decide the outcome. At the end, 2 champions from Argos left the field thinking all the Spartans were dead. However some of them were only wounded and on these grounds Sparta contested Argos' claimed victory. So then they went to all out war anyway.

In Japan, never. Possibly before the Muromachi period, but I've never seen any account of it happening. Duels happened, but something where 'champions' were sent out from rival armies to settle a large scale conflict (we're talking tens of thousands of soldiers on each side), never. It would have been a huge gamble to take, especially during the Sengoku period, where you had so many soldiers on each side - remember as well that, during this period of civil conflict, daimyo were raising armies from peasant conscripts, so a justification to save many lives just wasn't logical.

It could be possible that minor conflicts, such as small land disputes between small retainers, could be resolved (should the ruling daimyo wish) by a duel, though these duels would have been relegated to non-lethal fights.