For some time now, I have liked the symbol, Oroborus, and so I chose that symbol combined with the number "21" to represent my company.  The "21" is my favorite number and also stands for the 21st Century.
Oroborus, ("the tail devourer") also spelled Ouroborus, Uroborus and Auro Borus, is an archtypal form that appears across many cultures and has symbolic importance in several fields of knowledge.

The perfected form is a worm, serpent, snake, or dragon, winged or unwinged, that is either swallowing its tail (itself) or else just holding its tail in its mouth.  For some the difference in the symbology between merely holding the tail in its mouth and consumption of itself has meaning, with the latter being more esoteric, spiritual and representative of the eternal and regenerative nature of the symbol.
Three forms of Oroborus,
One is fish-like in nature
The Oroborus generally symbolizes self-sufficiency and cycles in Nature, regeneration, recursiveness, totality, completeness,
and
eternity.
The symbol has many meanings in different fields of knowledge:

In Psychology, Jung held the Oroborus as an archetype equivalent with the Androgyne, or unity of male and female principles.  In this it represents a fulfillment of completeness.

In Greek Philosophy, the Oroboros was the Aion, which Herakleitos likened to a child at play. To the Greeks, the Aion (from which our word "eon" is derived) defined the cosmic period between the creation and destruction of the universe.

In Alchemy, the symbol is linked with Hermes and figures prominently as a purifying glyph in that ancient mixture of science and sorcery.

In Orphic and Mithraic symbology, the Oroboros was called the Agathos Daimon or "Good Spirit" and was a symbol for the "Operation of the Sun."

In Norse Mythology, the serpent Jormungandr, from the myth of Yggdrasil, encircles the world or Midgaard.

In Indian Mythology, the dragon circles the tortoise which supports the four elephants that carry the world.

In Gnosticism, the symbol in the broadest sense is symbolic of time and the continuity of life. It sometimes bears the caption "Hen to pan" or "The One, The All" as in the Codex Marcianus, for instance, of the 2nd century A.D. It has also been explained as the union between the chthonian principle as represented by the serpent and the celestial principal as signified by the bird (a synthesis which can also be applied to the dragon). (Interestingly, in some Gnostic teaching there is the idea that this universal serpent "passes through all things" which reminds me of something along the lines of modern physicist's "Superstring" versions of "String Theory" which posits that all the universe is composed of such strings.  It would not surprise me if the structure of these closed strings was that of the Oroborus.)
Origin of the Symbol

The Serpent biting its own tail is first seen as early as 1600 years BC in Egypt. From there it moved to the Phonecians and then to the Greeks, who called it the Ouroboros, which means devouring its tail.

But the serpent biting its tail is found in mythology of many cultures throughout the world, including many of the Americas and the Far East prior to there ever being any contact with Greek or Near Eastern cultures.

The true origin of the Oroborus may be found in the stars, as our galaxy (the Milky Way) has been interpreted to look like a ringed serpent since time immemorial.  This may well be the inspiration of the symbol.
The symbol also stands for the cycles of creation and destruction that we see in the Universe.

From
Life to Death
and
Resurrection
If Space and Time are indeed curved as Einstein says,
then
the shape
that these take
will be the Oroborus.

-Eduardo Leaton Jr.
The 19th century German chemist Friedrich August Kekule was having great difficulty in trying to figure out the molecular structure of benzene.


I came upon a wedding that old families had contrived;
Bethlehem the bridegroom,
Babylon the bride.
Great Babylon was naked, oh she stood there trembling for me,
and Bethlehem inflamed us both
like the shy one at some orgy.
And when we fell together all our flesh was like a veil
that I had to draw aside to see
the serpent eat its tail.


-excerpt from "Last Year's Man"
by Leonard Cohen
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Myth refers to a serpent of light residing in the heavens. The Milky Way is this serpent, and viewed at galactic central point near sagittarius, this serpent eats its own tail. The Milky Way galaxy keeps a great time cycle that ends in catastrophic change. The sign of the Suntelia Aion is the sun rising out of the mouth of the Oroboros, which will occur on the solstice December 21, 2012 (12-21-12).
Is the End of All Things Near?

The Greeks called the End of the Age the Suntelia Aion Ancient historians and especially Plato referred to a cycle of catastrophe at the End of the Age. The AION was symbolized by the Oroboros.
This unusual double form, which happens to form the symbol of eternity turned on its side, connects the "above" with the "below" thus serving as a link between the spiritual and physical world.
One evening he was dozing before his fireplace and in his half-slumber he saw the flames leaping like snakes. According to his account, one came up and grabbed its own tail in its mouth and danced before him as if mocking him.  With a flash he awoke and understood immediately that the structure of benzene must consist of a closed carbon ring of (alternating) double bonded pairs.  This was the breakthrough he needed and it contributed greatly to the advancement of organic chemistry.