The divine mouse or shrew named Krauncha is widely considered to be the vahana of Lord Ganesha. The vahana or mount of any god serves as His divine carrier. The various Mahapuranas and Upapuranas also mention that a peacock, a horse, an elephant and lion have also served as Ganesha`s vahana. The Mudgala Purana mentions that the elephant-faced deity has a holy mouse as His vahana in 5 incarnations out of the 8 forms mentioned in the religious text. The mouse is usually placed near the feet of the Lord in most the sculptures. Furthermore, the Ganesha Purana, the Matsya Purana and the Brahmananda Purana mention that the divine mouse served as the vehicle of Ganesha.
According to a Puranic legend, Krauncha was a heavenly musician deity (Gandharvas). Once he was performing in the court of Lord Indra during a musical function. Several gods, deities and sages were invited to the event. Krauncha accidentally stepped on the foot of Sage Vamadeva who became enraged at his negligence. He cursed Krauncha to become a mouse (shrew). The Gandharva bowed down to the Sage with his hands folded and asked for mercy. But Vamadeva declared that he would serve as the mount of Lord Ganesha and will be relieved of his miseries. Therefore Krauncha metamorphosed into gigantic mouse. He started to destroy everything in his way. He also destroyed all the pages of the Puranas and the Vedas.
Later he went to the abode of Sage Parashara and started to damage it as well. Parashara then praised and prayed to Lord Ganesha and asked Him to stop the devastations of the mouse. Ganesha, also known as Vinayaka, tied a noose (pasha) on the gigantic mouse. The mouse was completely bound and it fell at the feet of the Lord. The cursed mouse bowed to the elephant headed deity and asked for His forgiveness. Ganesha forgave Krauncha and made him serve as the divine mount or vahana of the Lord.
Ganesha the mounted on the mouse but Krauncha could not bear the weight of the deity. The mouse then prayed to Ganesha to become lighter so that he might be able to support His weight. Lord Ganesha granted his wish and Krauncha has been serving as the vahana of Lord Ganesha since then.
Another legend mentions that Krauncha was cursed by Saubhari. Thus he was born as the son of Sage Kashyapa in the form of a mouse. Apart from this, various forms of Lord Ganesha are portrayed with different vahanas, such as, Mahotkata Vinayaka form has as either lion or an elephant as His mount, Mayuresvara form has a peacock, the vahana of the Dhumraketu form is a blue horse, a lion is the mount of Lord Vakratunda, the Vikata form also has a peacock, Lord Dhumravarna has a horse and the Vighnaraja form is depicted with Sesha, the divine serpent as His vahana.