The one particularly famous example that I always tell pupils about when they ask this question is prior to the Battle of Bannockburn. The leader of the Scottish forces, King Robert the Bruce (who appears in the historically awful film Braveheart) fought with Henry de Bohun, a prominent English knight.
A little background – Bannockburn was a key battle in the Scottish Wars of Independence fought in the late 13th and early 14th centuries. The English king, Edward II, sent an army north into Scotland to relieve a siege at Stirling Castle. The Scottish army met the English on an area of boggy ground and on the first day of the battle the famous encounter occurred.
An important source for the life of Robert the Bruce comes from the poem The Brus written in Scots (a language with similarities to English that was used in central Scotland) towards the end of the 14th century (possibly around 1378).
A section of this poem describes the single combat between Bruce and Henry:
Schyr Hanry myssit the noble king
And he that in his sterapys stud
With the ax that wes hard and gud
With sua gret mayne raucht him a dynt
That nother hat na helm mycht stynt
The hevy dusche that he him gave
That ner the heid till the harnys clave.
The hand-ax schaft fruschit in twa,
And he doune to the erd gan ga
And quhen the kingis men sa stoutly
Saw him rycht at the first meting
Have slayne a knycht sua at a strak
Sic hardyment tharat gan thai tak
That thai come on rycht hardely.
Quhen Inglismen saw thaim sa stoutly
Cum on thai had gret abaysing
And specially for that the king
Sa smartly that gud knycht has slayne
That thai withdrew thaim everilkane
And durst nocht ane abid to fycht
Sa dred thai for the kingis mycht.
Which in modern English is (roughly):
Sir Henry missed the noble king
And he [Bruce] in his stirrups stood
With the axe that was hard and good
Rendered him such a blow
That neither hat nor helmet could stop
The heavy hit he struck
So he cleaved his head in half
The hand-axe shaft broke in two
And Henry fell to the ground
And when the king’s men saw this
At the first encounter
Slayed a knight with such a strike
They gained courage so
That they came forward hard
When the Englishmen saw them come stoutly
They had great fear
And specially because the king
So smartly had the good knight slain
That they withdrew
And not one dared to fight
For dread of the king’s might.
The Scots went on to win the battle, thanks in part to newly developed defensive tactics, and in part due to poor leadership on the English side.
I have always thought of this story to be very appropriately ‘Hollywood’ – the opening combat between the ‘heroic’ king and an overconfident enemy and the ultimate victory of a smaller and less well-equipped army.
To answer the second part of the question, how common was it, I would venture that it is not very common. I struggle to think of many other examples of this type encounter but I am of course happy to be proved wrong by someone much more knowledgeable!