Was there a man who became immensely rich doing so repeatedly? A peasant that rose to fame and fortune by doing it? I am interested in pretty much any cases where something interesting like that occurred.
YES!
There was once a fine fellow named William Marshal who went from being the fourth son of a minor English noble to a major landholder in England, trusted aid of the kind and eventually regent to Henry III.
Whilst he didn't manage all that through ransoms he was infamous on the tournament scene in Northern France in his younger years - unlike the jousts often depicted in popular culture, these events consisted of groups of knights doing mock battle on a open field, during which the ultimate objective was to capture enemy knights in order to gain their horses and equipment and ultimately ransom them!
This method of ransom and combat was all a part of the order of Chivalry which the vast majority of knights tried to keep to in this period.
A bit more on Marshal: Marshal actually managed to earn enough prestige and wealth through tournamenting to establish his own coat of arms - no small matter at the time! He was serving the heir to the English throne at the time, known as Young King Henry. When his lord died in 1183 he actually went to the Holy Land for two years to fulfil his lords crusader vow before returning to enter the service of Henry II, King of England. He remained in royal service for the rest of his life, becoming Earl of Pembroke and a major magnate in England along the way.
Hope this helps!
Source: Studying Medieval/Early Modern History at degree level.
Recommended Books:
D. Crouch, William Marshal: Court, Career and Chivalry in the Angevin Empire 1147-1219 (Harlow, 1990).
R. W. Kaeuper, Chivalry and Violence in Medieval Europe (Oxford, 1999).
Well, King Richard the 1st (Coeur de Lion) was famously held to ransom by Leopold of Austria.
His ransom was, quite literally, a King's ransom. England was heavily taxed to pay it and a minstrel called Blondel was somewhat apocryphally credited with finding the kidnapped prince, thus earning some eternal fame.
Numerous sources of course but
http://www.nndb.com/people/426/000093147/
Is OK.
Its worth noting that although a statue of Richard I stands outside Parliament, and he is seen as the prodigal son in the Robin Hood stories, he couldn't speak any English and spent virtually no time in England at all.