Serpent Symbolism in  Western Painting

The Bible does not narrate kindly about the snake. The "serpent," symbolizes Satan.

snake - symbolizes Satan; the presence of evil, fall of man

snake in a fruit tree - signifies the mans fall from grace as well as  Satan's meddling in the affairs of men.

snake cleaved in two pieces - implies destruction of heathen evil.

a snake brazenly slithering across the middle of a thoroughfare or road - symbolizing the False Prophet leading the way to hell.

a devious serpent peeking out of a basket, urn or pot - a spiritual reminder of Satan's presence in unusual places.

snake coiled around a skull -  is a symbol for death, both of the body and the spirit.

Snakes in the Bible

Now the serpent was more subtle than any beast of the field which the Lord God had made. And he said unto the woman, Yea, hath God said, Ye shall not eat of every tree of the Garden?

And the woman said unto the serpent, We may eat of the fruit of the trees of the Garden:

But of the fruit of the tree which is in the midst of the garden, God hath said, Ye shall not eat of it, neither shall ye touch it, lest ye die.

And the serpent said unto the woman, Ye shall not surely die:

For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods, knowing good and evil.

And when the woman saw that the tree was good for food, and that it was pleasant to the eyes, and a tree to be desired to make one wise, she took of the fruit thereof, and did eat, and gave also unto her husband with her, and he did eat.
 

And the Lord God said unto the woman, What is this that thou hast done? And the woman said, The serpent beguiled me, and I did eat.
 

And the Lord God said unto the serpent, Because thou hast done this, thou art cursed above all cattle, and above every beast of the field; upon thy belly shalt thou go, and dust shalt thou eat all the days of they life.