We think of royal rulers as having numbers. The queen of England, for example, is Elizabeth II. But for most of the Middle Ages, kings with the same names were identified by nicknames, not by numbers.
Charlemagne, of course, was "Charles the Great," Carolus magnus (magnus being Latin for great). He was doubtless called this during his lifetime. His grandfather was also named Charles, often referred to as Charles Martel, "Charles the Hammer," because he was a great war leader and defeated a Muslim army in southwestern France in the middle of the eighth century.
These are the kinds of nicknames anyone would be proud to bear. But Charlemagne's father (Charles Martel's son) was known as Pippin the Short. One might wonder how Charlemagne managed to be so tall--he was a good six feet tall in an age when few men passed five and a half feet--with a short father. Well, Pippin the Short was married to Bertha Broadfoot, who one assumes was big in more aspects than just her shoe size.
Charlemagne's oldest son was Pippin the Hunchback. Now, it's not entirely clear that he actually was hunchbacked, but after Charlemagne divorced his mother (to marry the mother of the rest of his sons) he was removed from the line of legitimate succession. To add insult to injury, one of his younger half-brothers was also named Pippin, their grandfather's name. Pippin the Hunchback, feeling aggrieved, rebelled against his father and ended up being imprisoned in a monastery for the rest of his life. (One did not rebel against Charlemagne.) The "hunchback" nickname seems to have been made up after the fact to explain that he never could have succeeded to the throne anyway.
Charlemagne's eventual successor, Louis the Pious, got off fairly easy in the nickname department, but his own son, who became king of France, was called Charles the Bald, presumably not to his face. It is in fact not totally clear whether he really was bald or perhaps was just very hairy, and this was supposed to be a joke.
He is depicted above; you can't tell if he's really bald or not because of the crown. But if being bald is bad, how would you like to be Louis the Stammerer, the next French king? Or how about his son, Charles the Simple?
In comparison to the Carolingians, the Capetians had more innocuous nicknames, though Louis the Fat probably again would not have been called that to his face. But his grandson was Philip "Augustus," a nickname intended to invoke Caesar Augustus, and his grandson was Saint Louis. You don't get much better than that. Saint Louis's grandson was Philip the Fair, named for his blond hair.