The Hindu gods and goddesses use their own vehicles to travel. These vehicles actually represent the various energies that exists in the universe as well as in human beings. Each god or goddess is in-charge of a particular energy which he or she rides and controls at his or her will.
Ganesha - Mooshika the Mouse
Brahma - Hamsa when sitting or Seven swans
Vishnu - Garuda, the eagle and Adi Shesha, the Serpent
Shiva - Nandi, the Bull
Saraswathi - Hamsa or swan or sometimes peacock
Lakshmi - Lotus flower when seated and the owl
Durga or Parvati - Tiger or Lion
Yama - Buffalo
Adityas / Sun God - Seven horses / Agni
Indra - Elephant Airavata
Varuna - Seven Swans
Vayu - Thousands of horses
Ganesha's vehicle is Mooshika the Mouse. You may wonder how a small mouse can carry on its back a hefty personality like Ganesha. Here mooshika does not mean a mere mouse. It symbolises the darkness of ignorance because it is in darkness that the mouse moves about. Hence, Mooshika Vahana or Ganesha is one who subdues ignorance and dispels darkness. Ths also teaches us how humble and modest one should be. Ganesha in spite of his huge physical, mental and intellectual prowess conducts and carries himself so lightly that he can very well be carried by a very very small (compared to the size of Ganesha) and insignificant being-the mouse.
Brahma's vehicle is Hamsa which stands for the buddhi and for the creative and discretionary energies in man. The word " Hamsa" is a combination of two words, "aham"+ "sa" , which mean "I am He". This awareness that one is God exists only in enlightened persons. Rightly Brahma is the friend and philosopher of all the enlightened beings in the world and he has the power to give us this knowledge about our true nature. The bird hamsa is also very beautiful, peaceful and graceful. It is suggestive of the fact that Brahma is the master of all the beauty and grace in the world, and He can help us in our effort to acquire these qualities.
Shri Saraswathi, the consort of Brahma is shown riding either hamsa or the peacock. The peacock is a graceful and beautiful bird and is known for its dance before the rain. This denotes that Shri Saraswathi can immensely help those who want to pursue art and dance. The peacock also eats snakes, which symbolically means that she can help those who are accustomed to eating desires or for a better expression pursuing desires, by providing them with the divine knowledge and learning for which she is famous.
Lord Vishnu is seated on Adi Shesha, the primal serpent god, who represents the desire consciousness in us. Lord Vishnu can help us either to fulfill these desires or control them. When He travels, Lord Vishnu rides on Garuda, the giant bird. The bird represents the human thoughts which can fly in all directions at incredible speed. Lord Vishnu can help us to control our thoughts.
Shri MahaLakshmi rides on an owl called Uluka. The owl is a solitary creature, that remains awake in darkness and asleep during the day time. It rarely trust human beings and seldom seen in the company of any other bird. It in fact stays away from people as if it has no interest in the humanity.
Those who pursue riches should be aware of these negative qualities and pray to Shri Mahalakshmi so that she would inculcate in them the qualities of trust, generosity and social responsibility and would make them popular among people.
She would also help them come out of the darkness of ignorance, avarice and selfishness, which are generally associated with the pursuit of materialism. The owl is also regarded as an inauspicious image by the Hindus, who believe that if an owl visits a house in which people live, it is an ill omen.
Shri Mahalakshmi with her grace can remove all negative, inauspicious and adverse influences from our lives. If some one is suffering from adversity, they should pray to her because she, who controls all ill-omens and adversities can ward them off and bring them prosperity. Thus She has rightly been shown as using a rare bird like an owl as her vehicle.
Lord Siva rides the Bull, Nandi, which stands for the bullying, aggressive, blind and brute power in man. It also stands for unbridled sexual energy, kama. Only Lord Siva can help us control these and transform them.
His consort Shri Parvathi, variously called Uma, Chandi, Durga or Kali uses Tiger as her vehicle. Tiger stands for cruelty, mercilessness, anger, violence and hostility towards other beings. Pravathi with her grace can help man to control all these qualities in him and become an enlightened being like Lord Siva.