Ophidiophobia and herpetophobia are posh names for the fear of snakes. (You'll probably remember from the movies that Indiana Jones had such a loathing.) Usually this is a totally irrational fear but common nevertheless.
It is easy to understand why, in religious thought, snakes are an incarnation of evil.
First, some hissss-tory.1
Way back (way, way back) in the Garden of Eden, the Bible relates how a serpent appeared to Eve which led to the Fall of Man2. As we know, most snakes are harmless and shy of man, and this was a perfect cover for the Devil. A snake might be cunning but has neither the language nor intellect to do as described in Genesis. It was simply the instrument of the Devil3.
Since then, snakes have suffered the stigma of being dangerous, feared, and generally not very nice to find lurking under the bed.4
All of this seems rather unfair on the dumb snake, whose nature is to prey on other living things, just as the eagle does. Yet the eagle is generally considered magnificent (see Evangelists' Cross). We find similar prejudice in the avianism of the pigeon and dove.
But what is the meaning of a serpent on the cross?
One interpretation is that Christ, as the second Adam, has defeated Satan and saved man. Christians therefore might view the Serpent Cross as a crucifixion of the serpent thereby showing victory over the Devil. (Astrologers might view the same cross to symbolise Christian fanatics crucifying the Serpent Draconis, the symbol of knowledge.)
The most popular explanation however, is from the story of the Israelites who, whilst crossing the desert, began complaining against God and the prophet Moses. God punished the people by sending serpents among them and many were bitten and died before Moses interceded by praying to God to forgive them.
God instructed Moses to raise a venomous snake on a staff and all the wounded Israelites who looked on it were immediately healed5. The Serpent Cross draws a parallel with Christ, who was raised upon a cross for people to look upon and be healed6.
In French heraldry a cross charged with serpent heads at the extremities of its arms is known as Gringolée (also spelt Gringalee, Gringolly or Guivré).
Typically, serpent heads are seen in pairs and represent the salvation from sin. But in this case the heads are adorning a cross, which already represents salvation, so this is a curious combination.
Snakes shed their skin, to reveal a 'new' snake beneath. Taking this as 'rebirth' gives the association with salvation. But the cross itself has a much stronger association with salvation. See Meaning of the Cross.
The snake has been the symbol of a number of deities associated with healing, such as the Greek god Asclepius (Latin: Aesculapius), son of Apollo. The staff represents authority and the snake represents rebirth, as explained above. This symbol is now used by several medical associations and companies. (See also Medical Cross)
The Rod of Asclepius is similar to the caduceus, the sign for the Greek god Hermes, the ancient astrological symbol for Mercury, gods of commerce and thieves, and later became associated with alchemy. (See also Hermetic Cross)
It is not unusual to see a crozier with the image of a snake or serpent. Apart from the association with Moses lifting up the snake on his staff, the similarity with the rod of Asclepius links nicely to the role of bishops who are tasked with looking after those suffering from spiritual ailments.
From the 15th to 19th century there was a silver German coin called a Thaler. The pronunciation of thaler changed as the coin spread throughout Europe, and in English it was known as dollar.
One type of thaler coin was imprinted with a crucifix on one side and a serpent on the other side. The serpent was attached to a cross and the coin bore the inscription "NU 21", which refers to Numeri 21 (the fourth book of Moses in the Hebrew bible, Numbers chapter 21) and the story of Moses lifting up the snake on a staff5. From this symbol we have the dollar sign "$".