Ganesha, the most known god of India

Shiva and Parvati's son, Ganesha, is the "god of obstacles".
He is the first-born, considered symbol of wisdom. Your devotees are called Ganapatyas.
He has twelve names:
1. Sumukha: "The Lord full of grace"
2. Ekadanta: "The Lord who has only one prey"
3. Kapila: "The Lord of tawny color"
4. Gajakarna: "The Lord with elephant ears"
5. Lambadar: "The Lord with a prominent belly"
6. Vikata: "The Twisted"
7. Vighnanâsaka: "The Lord destroyer of obstacles"
8. Ganâdhipa: "The Lord Protector of Ghana"
9. Dhûmraketu: "The Lord of smoky color" with two arms riding a blue horse, Ruler of the Kali Yuga
10.Ganâdhyaksha: "The Minister of Ghana"
11.Bhâlachandra: "The Lord who uses the crescent moon on its head"
12.Gajânana: "The Sennhor with an elephant-faced".

These myths are from Hinduism.
He have an elephant's head. The history tells that he was created for Parvati, your mother, from her bath's paste, for protect her while she was bathed.
He loved his mother, and just obeyed her. Then, Parvati's husband (Shiva) wanted to enter, but Ganesha doesn't obeyed him, just your mother. Shiva was so angry, that cut off Ganesha's head.
Parvati was so unhappy and angry with the dead of his son, that asked Shiva for return Ganesha's life.
But, unfortunally, Shiva couldn't find Ganesha's head, and asked help for Brahma (god of creation).
Brahma told him, that he could return his life, if he give him a new head, the first head that he find.
And this head, was an elephant's head.
This way, he returned the life for Ganesha, and became his father.
That's the reason that Ganesha is represented with an elephant's head.
And now, he have to be consulted for all the decisions that people want to make.

Above, one of the ganesha statue.