In mythological world, the negative tendency of an individual is symbolized with animal nature. Gods in Indian mythology have been symbolized as living a positive behavior. Every God has a vehicle or Wahan. Both God and the Wahan symbolize how to live a positive life and how to control the animal tendencies.

A few examples:

Lord Ganesha’s vehicle is a Mouse. Mouse in mythology symbolizes greed and Ganesha is the one who removes obstacles. The spiritual meaning behind the two is “one should learn to control greed to tackle obstacles in life”.
Lord Shiva rides Nandi, the Bull. Bull symbolizes uncontrolled sexual desires. The duo signifies that to learn meditation, one needs to control sexual desires first.
Saraswati is the Goddesses of knowledge. She is depicted sitting on Swan, which symbolizes that to acquire knowledge, one must learn to control the power of discrimination or Vivek. A swan can drink milk and leave water from a mixture of milk and water.
Indra has complete control over the intellect. He is shown riding on the elephant Airavat. This symbolizes that intellect (Indra) can be developed by controlling Masti and madness (elephant).
Durga symbolizes the perfect woman. Ma Durga rides a lion. This symbolizes that to become a perfect woman, one must learn to control agitation or aggression (lion).
Lakshmi symbolizes wealth. Lakshmi riding an owl symbolizes that to earn righteously, one must learn to control the owl-like properties within us, which is not to get befooled.
Lord Vishnu (the doer) rides eagle or Garuda. Eagles are opportunistic predators. They eat almost anything they can find. This means controlling desires to eat unbalanced meals.
Krishna riding five horses means one needs to control the five senses.
Kartikeya rides on Peacock. This symbolizes that one should learn to control one’s pride (vanity) or ego.
Goddess Kali rides a black goat, Agni rides Mesha – a ram, Kubera, the God of wealth, also rides a ram. A ram is an uncastrated adult male sheep. Goat also signifies uncontrolled sexual desires but lesser than the bull.
Yamraj rides a buffalo, which is known for its rampant destruction. Lord Yama or Yamraja is referred to as the God of death, twin brother, lord of justice, Dharma Raja. One can do justice only if one knows how to control anger and aggressive behavior.