There are some stories in Puranas that connect Ganesha with Samudra Manthan or the churning of the ocean. The story begins with Devas (demigods) being defeated by the Asuras (Demons). Successive defeats at the hands of demons had a huge demoralizing effect of the demigods. The demigods approached Brahma for a solution.
Brahma directed them to Srihari Vishnu. The protector and preserver of the universe, Lord Vishnu asked them to churn the milky ocean with the help of the Asuras to retrieve amrut or elixir. Only amrut could help the Devas defeat the Asuras. Immortality was the only way to defeat Demons who had the blessing of Shukracharya who had the power to bring back the dead to life.
Vishnu told the Devas that the king of demons, Bali, was honest and trustworthy. He would not hesitate to participate in the Samudra Manthan which was beneficial to all the beings in the universe.
Devas approached Bali, the king of demons, who readily agreed to participate in the churning of the ocean.
Snake Vasuki was made the rope and the Mandrachal Mountain was made the rod. But it became impossible to keep the Mandrachal Mountain steady.
Devas and Asuras approached Vishnu for solution. Vishnu then told them that they had not offered prayers to Ganesha before beginning such a huge event. To succeed in any auspicious event, blessing of Ganesha is a must.
Devas and Asuras then offered prayers to Ganesha and took his blessings. Vishnu then took the form of tortoise and held the Mandrachal Mountain steady.