In these stories, the King often is not pleased that a commoner won the right to the Princess, and would often add extra hurdles. But in the end, the commoner does marry the Princess and does inherit the kingdom. So:
I address this question in depth in my book How to Slay a Dragon: A Fantasy Hero's Guide to the Real Middle Ages in the chapter called...unsurprisingly..."How to Win the Princess." (There is also, of course, "The Princess Saves Herself.")
For now, though, you might be interested in one of my earliest AskHistorians answers:
I'm not personally aware of dragon-slaying or drunken brawling that resulted in a marriage. However, at least in post-Norman Conquest England (wait, I know something about medieval England? what?), kings and barons could and did arrange marriages between their most loyal retainers and the daughters of other vassals who stood to inherit huge...tracts of land, or other wealth. The purpose was twofold. One, to prevent enemies of the king or baron from gaining either land to supply wealth, or land that could provide a strategic base for attack (in the case of nobles warring with each other). Two, to provide a tantalizing reward for solid service by the vassal--a reward that came without financial cost to the king or baron. Jennifer Ward argues that Henry I would even intervene in inheritance preferences so that a vassal's daughter he wanted to use as a reward would inherit ahead of her brother.
A most spectacular case is William Marshal, the famous English knight, under Henry II and Richard I. Henry promised the faithful but rather impoverished Marshal a marriage to superheiress Isabel of Striguil. This was potentially problematic for Marshal, because Henry was very much at war with his son Richard in Henry's dying days. Would Richard honor the deal? (Would Henry move to disinherit his own son?)
As the legend has it (although this might be propaganda or embellishment; the source is...biased), Marshal happened Richard by surprise one day, and became the only knight ever to unhorse him. Instead of killing the rebellious prince, however, Marshal only slew his horse.
It proved a fortunate--and fortune-ate--decision. Succeeding his father to the throne, Richard honored Henry's promise to Marshal of Isabel's hand in marriage. In one wedding ceremony, Marshal went from not even having enough money to afford the usual festivities surrounding marriage (he had to borrow it!), to basically being the king's wealthiest vassal.
Sources: Jennifer Ward, Women in England in the Middle Ages; David Crouch, William Marshal: Knighthood, War and Chivalry, 1147-1219