Immortality and the origin of death is one of the most popular topics of stories from around the world, actually. Often immortality is or can be conferred on average humans by eating or drinking a rare and special kind of food or beverage.
In the Islamic world you have the four immortals, including Khidir, the Green Man, who drank from the water of life and became immortal. Khidir’s tale shares some factors in common with the story of The Wandering Jew. You can read more about him and the other immortals here.
In China you have the Covert Eight Immortals:
whose power can be transferred to tools an used to destroy evil ro bestow life; as well as the Eight Immortal Scholars of Huainan, or the Eight Gentlemen, who aren’t deified or made supernatural in any way, as their “immortality” is a metaphor but I think that’s a fun play for fiction. As well as Emperor Qin Shi Huang, who famously spent much of his life searching for an elixir of immortality.
There are a fair amount of Native American tales that deal with this topic, too. The Boy Who Would Be Immortal is a Hočąk story, with analogues in Macmac, Menominee, and Potawotami, with their theme of fasting. If you plan to include immortals that blend with supernatural tales, Wendigo are certainly immortal (humans become Wendigo by breaking taboos or committing terrible crimes), as are Skin Walkers in Navajo legend.
In Vietnam, Hang Nga and Hau Nghe are made immortal by eating a special type of grass. Separate from this, you have the Vietnamese Four Immortals: the giant boy Thánh Gióng, mountain god Tản Viên Sơn Thánh,Chử Đồng Tử the marsh boy, and the princess Liễu Hạnh.
In both Hindu and Buddhist tales, the elixir of immortality is guarded jealously by the gods and Garuda, the mythological bird person, plays a very important role in these kind of stories in Southeast Asia.
Another linking theme is the Tree of Life, which many cultures have in common, from Yggdrasil to the Mesoamerican World Tree.
There’s a Yoruban tale about Oba Koso or Shango, who was forced to commit suicide by political intrigue but did not hang; The demigod Maui has many stories his quests involving immortality for himself and others in Tonga, New Zealand, Samoa, and many other Pacific Islands.
Also keep in mind, even if you’re going to allow Greek or Roman immortals to dominate your story-not all Greek or Roman immortals were white people. A notable exception is Memnon, an African (Ethiopian and/or Sudanese) king, who was killed by Achilles and mourned so deeply by Eos, his mother, that Zeus was moved to grant him immortality.
I highly encourage anyone else to add their favorite stories about immortality to this post!!!