Surprisingly yes, heres a link to a thread i made earlier with the exact same question if you want to read more about it. http://www.reddit.com/r/AskHistorians/comments/2755jc/was_trial_by_combat_ever_a_thing/

Yes, it was a real thing in medieval Europe. The practice was generally used when it was impossible for a court to determine which of two sides of a story were correct. The idea was essentially that God would come to the aid of the man who was telling the truth. There were other types of trials/ordeals as well, such as by water or by fire.

There is a relatively good semi-novelized account of the last trial by combat in France. It is called The Last Duel and was written by the medievalist Eric Jager. Jager fills in events that we have no record of with his own suppositions of what happened, but he is very careful to note where he is filling in without evidence and where he is getting information directly from his sources.

The story in The Last Duel takes place in 1386. A knight named Jean de Carrouges accused a squire named Jacques Le Gris of raping his wife, Marguerite. When the knight wasn't happy with the outcome of the original decision, he appealed to Parlement and the French king to allow him to fight Le Gris in a duel to determine the outcome. There are significant descriptions of the duel left in the French sources, including the formalities of the day, what the knight, squire, and lady (Marguerite) were wearing, who came to the duel, etc. If you're interested in what it would have been like, definitely check out Jager's book.

For a more academic treatment of ordeals, see Robert Bartlett's Trial by Fire and Water: The Medieval Judicial Ordeal.

There were also trials/ordeals in other cultures, although I don't know whether any had trial by combat specifically. There is a lot of work on Indian legal history and the ordeal in Hindu trials, for example. Richard Lariviere "Ordeals in India and Europe," Journal of the American Oriental Society, volume 101 (1981) 347-349.