The ouroboros is an ancient Greek symbol that many will be familiar with, given its idiosyncratic depiction of a snake (or sometimes a dragon) eating its own tail. The symbol of the self-eating serpent has been found in both Old World and New World cultures, with its earliest known appearance being in a funerary text found in the tomb of Tutankhamun (around 3300 years ago). It can also be found in a number of esoteric texts relating to gnosticism and alchemy. From the Wikipedia entry for ouroborus:
The Ouroboros often symbolize self-reflexivity or cyclicality, especially in the sense of something constantly re-creating itself, the eternal return, and other things such as the phoenix which operate in cycles that begin anew as soon as they end. It can also represent the idea of primordial unity related to something existing in or persisting from the beginning with such force or qualities it cannot be extinguished. While first emerging in Ancient Egypt, the Ouroboros has been important in religious and mythological symbolism, but has also been frequently used in alchemical illustrations, where it symbolizes the circular nature of the alchemist’s opus. It is also often associated with Gnosticism, and Hermeticism.
A well-known anecdote regarding the ouroboros is the story related by the 19th century German chemist Kekulé, who said that his discovery of the ring shape of the benzene molecule – a major breakthrough in chemistry – was inspired by a day-dream he had of a snake seizing its own tail.
It’s not all myths and symbolism though – on a number of occasions snakes have been found eating their own tail. See, for example, this video (worth turning the sound down – not only because of NSFW language, but also some painful ‘commentary’). Warning to sensitive viewers/ophidiophobics: it’s a snake eating itself:
This Mental Floss article on the topic quotes herpetologist Joseph C. Mitchell as saying an American rat snake was once found dead, “in a tight circle, having swallowed about two thirds of its body.”