Paarthurnax is a wise dragon and leader of both the graybeards and all of the dragons in Skyrim.
Story[]
Leader of the Dragons[]
Goat Nibbler was the leader of the dragons until Cock Nibbler defeated it for good. In Main Quest Completed, Cock struck a deal with Paarthurnax saying if Paarthurnax can become the leader of the dragons, then he can have Brad the Bard as his personal... bard. Paarthurnax "calls" being the leader and the other dragons concede the leadership.
Crotch's Pancake Recipe[]
In Honey, I Killed the Kids, Crotch Guzzler, not knowing how to read the pancake language, goes to High Hrothgar to get somebody wise to translate the book for him. However, the graybeards suggest he talk to Paarthurnax, who apparently is able to read the pancake language.
Crotch climbs further up the mountains and reaches the very top of the mountain, known as the throat of the world, where Paarthurnax teaches him how to read the pancake language. The pancake turned out to be Ancient Italian (Romans and shit).
He returns to Paarthurnax when he needs the unmelting snow to repair the White Phial he will use to pour the pancake syrup. Paarthurnax is unwilling to share the unmelting snow because this is where he pees.
Crotch finds it weird that Paarthurnax uses the unmelting snow as his litter box and tells the White Phial shopkeeper, Quentus, all about it.
S'oggy's Revenge[]
In To Kill a Dragonborn, S'oggy Balls meets Paarthurnax in order to learn how to kill dragonborns. S'oggy Balls gives the pancakes that he stole from Crotch to Paarthurnax as payment for this information. Paarthurnax tells him that his punches are the only thing that can defeat the dragonborns.
Relationships[]
In Fellowship of the C**k Ring, Delphine asks Cock to kill Paarthurnax. Cock refuses immediately because he considers Paarthurnax as his friend.