Dampé is the name of four Hylian characters and one Shiekah character in The Legend of Zelda series. It is most likely each character is related, as they all look quite similar to one another and continue to hold the same profession, apparently passed down through their family. A genetic disorder affects them, as they all possess physical deformities similar in appearance to craniodiaphyseal dysplasia. His look may be inspired by either Sloth from The Goonies or Quasimodo from The Hunchback of Notre Dame.
The Minish Cap
During the Force Era (the era right after the formation of the kingdom of Hyrule), the first known Dampé had come to serve as gravekeeper within the Royal Valley, found in western Hyrule. Although it is unknown how he received this job, it may have something to do with the fact that his deformed face frightens regular Hylian citizens, forcing him to live outside of crowded areas.
This Dampé was friendly, and enjoyed collecting and fusing Kinstones. When the hero of size appeared in the world, he relinquished his graveyard key to the child.
Ocarina of Time
The second known Dampé appeared on the records during the Era of the Hero of Time. He has moved into Kakariko Village after its founding by the Shiekah Impa, choosing to reside in a shack within the village's graveyard. He is a morbid individual, and makes money on the side by digging the graveyard grounds for a few hours every night in a "game" he refers to as "Dampé's Heart-Pounding Gravedigging Tour." Although children seem to like him, he is grumpy if woken up during the day.
At some point during the seven years between the Child and Adult eras, Dampé found a hookshot during grave tending that he decided to keep with him as a keepsake. However, he since has passed away, most likely from complications from his disease and chose to have the hookshot buried with him. When the Hero of Time Link realized he required the item, he disturbed Dampé's grave. However he discovered that Dampé had become a ghost and had to race him to claim the item. Even though Link was unable to actually beat Dampé in the race, he still rewarded the hero with the hookshot for simply keeping up with him.
In the alternate dimension known as Termina (which may or may not have actually been purgatory), the Hero of Time, now reverted to his childhood state and no longer remembered as a hero, finds himself trapped in this realm during a time when the entire realm itself is nearing Armageddon.
This alternate version of the Dampé of the era was essentially the opposite of his Hyrule counterpart, living a diurnal life (being awake and active during the day and sleeping during the night) and was a coward, being terrified of the ghosts and monsters that haunted the Ikana Graveyard that he had come to tend. He also has a general distaste for Bad Bats and possibly other Keese subspecies.
He appears to know who Captain Keeta is, a giant Ikanan who had been transformed into a Stalchild long ago. This is evident if Link chooses to wear the captain's hat around Dampé, who will then confuse him for a ghost and panic.
Whereas the Hyrulean Dampé only entered the underrealm of the graveyard after death, the Terminan version enters the realm on the Final Day after finding a path to it through his own hut, looking for a bottle for unknown reasons. It is too dark for him to find anything but when Link shows up with his new fairy Tatl, her light allows him to try digging for the treasure he desires. Unfortunately his disturbing of the ground leads to the emergence of a Big Poe which frightens the coward off. As Dampé flees and Link is left to fight the Poe alone, Link claims the treasure the gravekeeper had been seeking for himself.
A Link Between Worlds
With the timeline split into three, another pair of Dampé appear in both Hyrule and its twilight realm counterpart, Lorule during the Era of Light and Dark in the Decline of Hyrule timeline. Both the Hylian and Shiekah versions maintain a graveyard north of the castle and speak in the third person.
When Yuga seals the Santuary entrance to prevent interference against his turning Seres into a painting, it is the Hyrule Dampé who informs the blossoming Hero of Worlds Link that it is his graveyard that holds a secret entrance back into the Sanctuary.
It is theorized that the Lorule Dampé may in fact be undead, as he possesses a distinctive purple tint.
Four Swords Adventures
In a different timeline - that of the Twilight Realm - a final, humpbacked Dampé appears later; this is currently the latest Dampé to appear chronologically, during the Shadow Era. At this point Dampé's family has moved into the swamp to watch over a graveyard found here. Although he had no true affect on the four Links' journey, he did inform them about the existence of the Forest of Light.