It seems to me they could just break the law, kick some ass and do it again! Also, how realistic is the concept of trial by combat? Could anyone invoke the right? I would assume that if they could, every guilty person would do so. I mean, if you're going to be hung you might as well try and fight someone. I don't have a particular era or country in mind because I don't want to limit responses to a single point in time and/or country. If you could elaborate how trials by combat worked - perhaps the law surrounding them (or anything of interest) I'd also really appreciate it! Thanks in advance guys
To answer your question directly:
Wager of battle (as it's called in English law) was only available to nobles in criminal cases, so random sellswords couldn't just go around committing crimes and getting off scot-free.
A more in-depth overview
When William the Bastard, Duke of Normandy, came over the English Channel and conquered England in 1066, he brought over Continental legal traditions and institutions with him. This included wager of battle.
Wager of battle was one of three major methods of settling legal disputes in medieval England. The other two were trial by jury and trial by ordeal (subjecting a defendant to an unpleasant experience-- like grabbing hot coals-- and seeing whether the will of God saves them). Trial by ordeal was banned around 1219, leaving trial by jury and wager of battle as the two major methods of dispute resolution.
Wager of battle was available in both civil and criminal cases. It was common to hire a champion (a sellsword) to serve as a litigant's representative during a trial by combat, even though having a paid champion was officially illegal. Sounds good, right?
Well, there's one catch: the loser of a trial by combat was declared an outlaw, in the Robin Hood sense. To be an outlaw in medieval England was to be declared persona non grata by civilized society. Since no one wanted to be declared an outlaw, wager of battle gradually died off and was replaced by the trial by jury. By 1300, it was was virtually extinct.
That said, Parliament never entirely abolished the right to a trial by combat until 1819. The last recorded request for a trial by combat was Ashford v. Thornton, 106 ER 149 (1818).
Sources:
Lewis Powell, Jury Trial of Crimes, 23 Washington & Lee L. Rev 1 (1966)
Peter Leeson, Trial by Battle, 3 J. Legal Analysis 341 (2011).
George Neilson, Trial by Combat (1890). It's one of the canonical texts on the subject, despite its age.
Can we still do this now? Just curious, also i saw a report of a court case where the defendant wanted a jury by combat but the judge denied his request.
There was a thread on trial by combat just the other day, I suggest you read it: http://www.reddit.com/r/AskHistorians/comments/25ci59/was_trial_by_combat_an_actual_thing_in_medieval/
Basically, it wasn't all that common. So the short answer to your question would be "no."
Please remember that Game of Thrones is not a documentary, it's a fantasy world with dragons, magic, and plenty of other odd stuff. It's not a good source for historical accuracy.