Lord Ganesha
Remover of Obstacles
Ganesha, otherwise known as Ganapati, is the remover of obstacles and the God of knowledge, writing, and astrology. He is normally prayed to first to make sure the prayers are successful. He is the eldest son of Lord Shiva and Mother Parvati. He is one of the most universal gods of Hinduism, nearly all Hindus pray to him. He also is likely the most popular Hindu god amongst non-Hindus since he has pop-culture appeal.
Why He Has An Elephant Head
He has the head of an elephant. Shiva, the father of Ganesha, was away meditating for a long time in the mountains as he tends to do. While he was away his wife, Parvati, had a son. She named him Ganesha. Parvati likes to take long baths and so she told Ganesha to guard the entrance of her bath house and not let anyone in, she did not want to be disturbed. So along came Shiva, just having come down from the mountains. He saw Ganesha standing in front of the doorway to the bathhouse, where he knew Parvati would be. He did not realize this was his new son, and Ganesha did not realize this was his father. Neither had yet met. So Ganesha would not let Shiva enter as he was instructed by his mother. Shiva got very angry at this. Finally Shiva glanced at Ganesha with his firey third eye, burning Ganesha's head off. Hearing the commotion outside Parvati came out and saw what had happened to Ganesha. She was very upset and informed Shiva this was his new son. Shiva instructed a servant to go out and take the head of the first being they saw. The servant came back with the head of a elephant. Shiva attached the head and used his mystical powers to bring Ganesha, now with the head of an elephant, back to life.