The crest of the Elric Brothers is in fact not a family crest, but more likely a sign which alchemistic teaching they both are following. At present, there are three people with it - Edward and Alphonse Elric and their teacher Izumi who has it tattooed on her left breast. (It could be Izumi's own design or that of an alchemistic order)
So, what do we see? A cross, a crown with wings and and one snake - the design is actually a merging of two alchemistic symbols that can be found in Nicolas Flamel's* "The Figures of Abraham the Jew".
The winged caduceus of Mercurius
In A Dictionary of Symbols we find:
"For the Romans, the caduceus served as a symbol of moral equilibrium and of good conduct. The wand represents power; the two snakes wisdom; the wings diligence; and the helmet is the emblem of lofty thoughts... According to esoteric Buddhism, the wand of the caduceus corresponds to the axis of the world and the serpents refer to the force called Kundalini, which, in Tantrist teaching, sleeps coiled up at the base of the backbone - a symbol of the evolutive power of pure energy. Schneider maintains that the two S-shapes of the serpents correspond to illness and convalescence. In reality, what defines the essence of the caduceus is the nature and meaning not so much of its individual elements as of the composite whole. The precisely symmetrical and bilateral arrangement, as in the balance of Libra, or in the tri-unity of heraldry (a shield between two supporters), is always expressive of the same idea of active equilibrium, of opposing forces balancing one another in such a way as to create a higher, static form. In the caduceus, this balanced duality is twice stated: in the serpents and in the wings, thereby emphasising that supreme state of strength and self-control (and consequently of health) which can be achieved both on the lower plane of the instincts (symbolised by the serpents) and on the higher level of the spirit (represented by the wings)."
The two serpents also represent male and female - balancing each other out. A hermaphrodite was seen as a perfect being in alchemy and in every alchemistic process you a male and female semen for a transmutation was needed.
A caduceus is also symbolic for immortality and other gods besides Mercurius/Hermes carried one.
The crucified snake
The symbol for "fixing the volatile" or making the Elixir of Mercurius (a legendary curative that is made by removing the volatile -or poisonous elements).
Also, it is a metaphor for an important mental process to an inner-state-of-mind required for the production of a philosophers' stone: to overcome one's base or materially inclined nature.
* Nicolas Flamel (1330-1417): french alchemist. Working as a scribe in Paris, he came upon a book supposedly written by Abraham Elezear. Next to Greek texts were interesting, but to Flamel, disturbing illustrations (virgin getting eaten by snakes, the crucified snake, aso.) For years, he and his wife Perenelle tried to solve the book's puzzle - with the help of a Master Canches, they were able to interpret the illustrations.
In 1392, Flamel and his wife were able to produce a "first agens" and produced with it silver and gold. Most of the produced treasures were donated to the church**.
** In alchemistic belief the making of any alchemy is not only a chemical process, but also a spiritual one - in order to make a Philosophers' Stone you need to achieve a state of mind that is in balance with itself and totally un-selfserving. And by then, you don't really need such a powerful thing anymore.
The Alchemy Web Site