Greek

Here, I’d like to focus on how animals are associated with certain gods in Greek mythology. Some of these associations arise from myths surrounding a particular god, as in the case of Poseidon, the god of the sea. Others are related to the areas the deities are reigning over. Curiously, some animal associations lack any real or recorded ties to the deity, but are still commonly depicted with them, and symbolise some of their attributes.

Poseidon, lord of the sea and god of horses
As ruler of the sea, one would expect Poseidon to be depicted with multiple sea creatures. However, he is most often captured in paintings with horses.




The Triumph of Neptune (detail), by Nicolas Poussin (1594-1665), French Baroque painter. Note that Poseidon was equivalently known as Neptune to the Romans. (http://www.mythindex.com/greek-mythology/P/Poseidon.html)

In fact, the Greeks worshipped him as Poseidon Hippios, the lord of horses, and there are several myths about him fathering the first horse. In one of these myths, he once slept with Medusa and she thus conceived the winged horse Pegasus. In another, he assumed the form of a stallion and mated with a goddess who had turned herself into a mare to escape him, hence producing Areion, the divine horse of Adrastos. Perhaps the content of such myths is why horses are used to symbolise sexual energy today.

Artemis, goddess of wild animals and the moon
Artemis, the virgin huntress, or the goddess of the hunt and the wilderness, has often been portrayed as a “young, tall, vigorous maiden who wears a short tunic reaching to her knees, carries a bow and quiver, and is often accompanied by a stag or doe.”



In the above image, Artemis is depicted on a type of Greek pottery called the stamnos, together with stags drawing her chariot and a hare in front.
Today, the deer as an animal symbol represent gentleness, which does not seem to have much connection with Artemis in Greek mythology.


Athena, goddess of war, wisdom, divine patroness of arts and crafts
The virgin goddess Athena is the patron goddess of Athens. She has been represented in art fully-armed with ornate helmet and long spear, and sometimes with an owl perched on her shoulder.




Replica of Athena Parthenos in Nashville, by Alan LeQuire. (http://www.nashville.gov/Parks-and-Recreation/Parthenon/Athena.aspx)


There is no myth recording how the association between Athena and the owl came to be, but owls are now associated with wisdom and inituition, possibly in part due to its historical representation of Athena. 


References:
Hard, Robin. The Routledge Handbook of Greek Mythology. London: Routledge, 2004. Print.