Genesis 3:14 - 15 says,"So the LORD God said to the serpent, 'Because you have done this,
Cursed are you above all the livestock
and all the wild animals!
You will crawl on your belly
and you will eat dust
all the days of your life.
And I will put enmity
between you and the woman,
and between your offspring [a] and hers;
he will crush [b] your head,
and you will strike his heel.'"
Many think that before the Fall snakes not only had feet, but maybe even wings. After the curse it was made the symbol of everything dubious and low. God stripped it of its honor for being a tool used by the fallen Lucifer. Since then the snake has been used in many cultures and religions as a symbol of death, mortality, and evil. Also it is interesting to think about the fact that the snake has been set at the head of many false religions. Satan is still trying to use the snake to deceive people and put himself on the same level as God. In ancient Greece the temple of Apollo at Delphi was originally named Pytho for the Python, a snake that was associated with Apollo. In Egypt it symbolized the god Ra and every temple had a space alloted for snakes. In Rome they kept one sacred snake attended to by the vestal virgins. When the snake refused food from one of its care givers, it was thought that she had lost her purity; she was killed.
The first Messianic prophesy is given to us here. God first cursed the physical serpent, but then moved to the spiritual one. Essentially it says that between unbelievers and the Messiah there will be tension and strife. Also this passage tells us that even though the Messiah will be caused to suffer by the serpent, the serpent will be destroyed by the Messiah. Jesus Christ fulfilled this on the cross where he was caused to suffer, but in the end He conquered Satan and Death by returning to life. In Romans 16:20 Paul tells us, "The God of peace will soon crush Satan under your feet.The grace of our Lord Jesus be with you." This reminds us who believe now that because of Christ's finished work on the cross we are also of the woman's seed. This means that we will be at odds with unbelievers in our world for they are part of the serpents offspring.
Info on snake worship
MacArthur Bible Commentary