Remember that scene in Troy where everyone gathers around to watch Paris and the other king (I forgot his name) fight or when Hector (I think) fights Achilles? Are these just used in myths? A creation of hollywood?
I'll limit the first part of my answer purely to the Bronze Age and Iron Age Mediterranean world. They're not a creation of Hollywood, since the battle between Hector and Achilles and the fight between Paris and Menelaos both take place in Homer's Iliad (although the movie dramatically changes the outcome of one fight...).
Homer may have somewhat exaggerated the use of champion warfare. The Iliad, after all is a story about heroes. And stories of heroes like Ajax and Hector duking it out make for good entertainment. However, we do know that Homer faithfully recorded many details about Bronze Age warfare. The use of chariots, throwing spears, and oxhide shields are all mentioned in homer and have all bee corroborated by historical evidence. In other words, there's reason to believe Homer may have been telling the truth about the (occasional) use of champion warfare during his time period.
Later in history, we do have definite examples of champion warfare. For examples the [Battle of the Champions] (http://www.ancientgreekbattles.net/Pages/54620_BattleOfChampions.htm) in 546 BC, which pitted Argive and Spartan champions against each other in an inconclusive battle.
There's also Livy's mention of the famous Horatii and Curatii triplets who fought each other in single combat during the years after Rome's founding. There's also the famous Horatius Cocles who single-handedly held off invading Etruscan forces trying to cross the Tiber.
It was indeed a thing that was done, though not nearly as prevalently as depicted in modern media.
Sometimes, a battle was opened with both sides observing a single combat between two champions. These champions were never part of the command structure of the armies, though were not peasant conscripts either. This single combat did not decide anything, but it would give a morale boost to the winning side.
In pitched battle, individual warriors would sometimes seek out specific other warriors for revenge or to capture for ransom. This would not be occasioned by everyone else stopping to watch and would rarely devolve into single combat, instead more of a team affair with each side's companion fighters contesting in the middle of a chaotic melee.
Judicial, "trial by combat" type affairs were common off the battlefield, however, and were often single combat observed by an audience.