Lord Ganesh is the elephant-headed God, with one tusk. There are several legends of how he got his elephant head. The following is a fascinating one.

One day Parvati, Shiva's beloved wife, instructed Shiva's attendant Nandi not to let anyone in while she was taking a bath. A little later Shiva arrived wishing to enter. Nandi was in a dilemma as how to stop his master. When Shiva entered the chambers Parvati was not ready to receive him. She was upset and wondered why Nandi had not obeyed her command. She complained to Shiva but Shiva did not take the matter too seriously. He was amused to hear that Parvati had asked Nandi to stop him from entering his own home. Parvati was annoyed. She shared her feelings with her friends. They teased Parvati by saying that she had no attendant of her own. All attendants considered Shiva their true master.

One of Parvati's, friends came up with the idea to create a person who would owe his first allegiance to Parvati and not to Shiva. So Parvati gathered the saffron paste (used at the time of bathing), from her own body and created a boy. The boy was handsome and strong. She gave the boy life and bugged him dearly.

 
"You are my son, my very own son, I do not have anyone else to call my very own" said Parvati. Then Parvati gave the boy a staff and asked him to guard the door, "Do not allow any one to enter without my permission."

A little later Shiva arrived and wondered who the boy could be and why was he there. His attendants did not know either. As Shiva approached the door, the boy stopped him. Shiva tried to explain to the boy that he was Parvati' & husband and he had the right to enter without asking any one. The boy said without hesitation, "no one enters these halls without my mother's permission." When Shiva ignored him, the boy hit him with his staff. Shiva was furious. He tried to fight the young boy and realized that he was no ordinary boy. Shiva asked his attendants to capture the boy but single-handedly, the boy defeated all of them.
  

The messenger returned to Shiva and humbly informed him what the boy had said. Shiva's pride was hurt. Shiva was so angry that he sent his entire army to capture the boy. Parvati called for her other powers, Kali and Durga. She asked them to stand beside her son. Shiva's army lost the battle and the attendants ran for their lives. Shiva then called Vishnu to join him in defeating the small boy. This was not a fair fight. While the boy was engaged in fighting with Vishnu, Shiva threw his Trident and beheaded the boy. After the head rolled off, Shiva realized his mistake.
  

  
When Parvati heard of the unfair fight she decided to destroy the world. Brahma humbly approached Parvati, seeking for mercy to save the world. Parvati agreed on two conditions, "My son must regain his life and he shall be worshipped before any of the other gods." By that time Shiva had calmed down and apologized for his rash behavior. He agreed to bring the boy back to life. He asked Brahma to go north and bring the head of the first creature that crossed his path. Brahma left with his party and soon brought back the head of a strong elephant. The head was then fitted to the body of the boy and Brahma sprinkled water on it. The boy came to life with an elephant's head on his shoulder. Parvati embraced her son with joy. She then turned to Brahma to fulfill her second condition. Indra and the other gods brought Shiva to Parvati. Shiva apologized for his arrogance and declared "Hence on, this valiant boy will be my son. He will be respected as any other God and will be worshipped before any other God. He will be called Ganesh, the chief of my Ganas or attendants, and also Vigneshwara, the remover of all obstacles.