Ganesha acquired his head through varying methods in different stories. In one, Shiva decapitated him because Ganesha refused to allow him to enter the bath while Parvati was bathing. Shiva had to give him the new head to placate his wife. In another version, Parvati showed the child off to Shiva, whose face burned his head to ashes, which Brahma told Shiva to replace with the first head he could find--in this case, that of an elephant. The lack of a second tusk is explained by a different myth. An avatar of Vishnu, Parashurama, once went to visit Shiva but the way was blocked by Ganesha. Parasurama threw his axe at him and Ganesha, knowing the axe had been given to him by Shiva, allowed it cut off one of his tusks.
In India, especially in the state of Maharashtra, there is an important festival honoring Ganesha. It is celebrated for ten days starting from Ganesh Chaturthi. This was introduced by Balgangadhar Tilak as a means of promoting nationalist sentiment when India was ruled by the British. This festival is passionately celebrated and in culminates on the day of Anant Chaturdashi when the idol of Lord Ganesha is immersed into the most convenient water body. e.g. in Bombay the idols are immersed in the Arabian Sea. In Pune the idols are immersed in the Mula-Mutha river.