Ganesha is known as Ekadanta,the one with a single tusk.The first pertains to his battle with Parashurama,who was the 'Avtaar' of Vishnu,As a  human on earth, he meditated on Shiva and obtained the devine axe, parashu,with whose help Parasurama waged wars against all the erring princes and cleared the world of their evils.

Deeplyindebted to Shiva,Parasurama then came to mount Kailasa to pay obeisance to his mentor Ganesha,who was guarding the entrance to his father's chamber,would not let him in,saying he had to wait till he gets the permission from his father,Shiva.Parasurama felt that he,the devotee,needed no permission. 

When Ganesha still refused to give in,Parashurama,who was always very hot tempered struck Ganesha's tusk with his axe and broke it.Shivaand Parvati appeared before him and chastised him.
Parashurama then apologised and worshipped God Ganesha.Ganesha then forgave Parashurama and gave him blessings.