At the Battle of Bosworth Field, August 22nd 1485, King Richard III of England was killed in battle against Henry Tudor (soon to be King Henry VII). While actual combat between the then-king and the future king did not occur, both were present on the field and engaged in combat, and got very close to engaging one another in personal combat. At the time Richard was killed (by Henry's bodyguards) he was attempting to charge Tudor and engage him in combat to turn to the tide of the battle (which was going against Richard). He managed to kill a couple of well known soldiers accompanying Tudor, but didn't get quite close enough to engage him in personal combat. He died rather famously and violently, struck down by Tudor's Welsh bodyguards. Archaeological excavation of Richard's body last year confirmed the circumstances of his very violent death. This is the major example that I can think of, of a circumstance where there was a near-personal combat of the type you are asking about. I know citing Wikipedia is frowned upon at AH, but they do have a rather solid article about Bosworth here (http://en.wikipedia.org/wiki/Battle_of_Bosworth_Field) if you are unfamiliar with the battle.

At the battle of Bannockburn in 1314, Scotland's King Robert (the famous Robert the Bruce) was ambushed and attacked in front of the lines before the battle began by Henry de Bohun, an English nobleman who was a major figure in the English army. King Robert was not well armed or armored (he just had an ax) as he wasn't expecting a fight, but as Bohun charged with a lance he pulled himself up on his horse and split his enemy's head apart with an ax - in full view of both armies.

While only one of the combatants was a king, it was dramatic enough for historians to believe that it helped turn the tide in the Scots' favor, which is especially important because it helped ensure Scottish independence for hundreds of more years.

It was also totally badass.

You may be interested in some of the discussions in the 'Did leaders participate in battles?' section of the Popular Questions pages (as found in the sidebar).

If you'll forgive an older example, Alexander the Great nearly engaged Darius III (Emperor of Persia) at the Battle of Gaugamela in 331 BC. Alexander formed his Companion Cavalry (elite Macedonian shock cavalry, and royal bodyguards) into a wedge and personally led the charge through the ranks of Darius's army (which was already weakened) and straight for Darius himself. Alexander and the Companions engaged Darius's royal guard but Darius himself was able to escape.

Darius was assassinated before Alexander had another chance to fight him. Rather than rejoicing, Alexander gave his enemy a proper burial and executed his assassin.

There's evidence (most notably in the Carmen) that Harold Godwinson was not killed by a chance arrow in the eye (as frequently told and depicted on the Bayeux Tapestry) but rather killed and dismembered by Duke William and his buddies, and that the arrow story was merely part of the propaganda machine following the Norman Conquest to paint William in a less brutal light. This was particularly important following the Harrying of the North.

While William was not really a king by title at that point, I'm assuming your question is more concerned with the people leading the battles than the titles, as King wasn't a particularly common title -- nor one that guaranteed any sort of real power or martial presence -- through much of the Middle Ages.

EDIT: Also, it's worth noting that certain kings were considered "warrior kings" and frequented the frontlines in battles they participated in. There are various contemporary (or near-contemporary) sources, both Muslim and Christian, that attribute multiple frontline rallies to Richard I during the Third Crusade.

In 1460 at the battle of Northampton during England's War of the Roses, Edward the Earl of March, went to battle against forces led by King Henry VI. At the end of the battle Edward's forces captured King Henry VI, and in early 1461 Edward was declared Edward IV the King of England. Also interesting to note that after Henry was captured his wife, Queen Margaret of Anjou, attempted to rally and led his forces against Edward before being forced to flee to France with her son.

Eventually Henry VI was restored to the throne and Edward was forced to flee to Burgundy. In 1471 Edward again led forces against Henry VI, capturing him in London and then engaging in battle at Tewkesbury. In this battle Henry's heir, another Edward, was killed in battle along with Warwick the Kingmaker. At Edward's side were his two brothers, one of whom became King Richard III - who was killed at the Battle of Bosworth Field by the bodyguards of the future Henry VII.

Alison Weir's War of the Roses is a great text if you are interested in the other battles fought during the time, most of which were led by upper nobility. For more on Henry VII, William Penn's Winter King has great information about his early years as King (including Bosworth Field) but the test is rather lacking when it comes to the events leading up to Bosworth Field.

Does a revolt count? In the tenth century Bardas Phokas has rebelled against the byzantine emperor Basil II and declared himself emperor.

Phokas had one a previous engagement against an enemy general, who had also rebelled against basil, a few years earlier by charging that general in the middle of battle and striking him on the head with his sword.

During this confrontation he thought he could do the same. He saw Basil in the front lines instructing his trips and decided to attack. Bardas gathered around him a few fierce Armenian warriors and charged out from his lines.

Basil appears to have been caught off guard. Immediately he drew his sword and clutched an icon of the virgin Mary in his hand.

Has Bardas drew closer, his arm suddenly lowered, his sword dropped, he swayed and fell. Bardas was dead. The 11th century historian Michael Psellos relates that no one knew what happened, some rumored that he was poisoned , sick or that God had struck him down. The last modern historical reason I've seen for it is that he merely suffered a stroke.