The Indian Puranas mention that Lord Ganesha is praised and worshipped by the demons or asuras. The religious scriptures mention that once there was a sage named Gritsamada. He was the son of Shunahotra and belonged to the Bhrigu family. The sage was always engaged in performing tapas on Lord Ganesha. However, one day a child (Tripurasura) emerged from his sneeze which immensely surprised the ascetic. The child then requested sage Gritsamada to raise and take care of him. The child also announced that after he grows up he will conquer the three Lokas or worlds.
Gritsamada then requested the child to go to the forest and meditate on Lord Ganesha. Hence the sage told the Ganesha Mantra to the child and sent him to the forest. Tripurasura then went to a remote part of the forest and began to worship Lord Ganesha. He performed tapas for a long period and meditated without consuming food. Lord Ganesha became pleased with his devotion for the Lord and appeared before him. The elephant headed deity advised the child to ask for a boon. Tripurasura told the Lord that he was greatly influenced by Ganesha`s lustre. The child requested the deity to bless him with a boon to be the ruler of the three worlds. Lord Ganesha was pleased with his tapas and granted him the desired boon.
There is another myth that is related with the adoration of Lord Ganesha by the demon Banasura, also known as Bana. The asura was the son of Bali and had a thousand arms. The Brahmavaivarta Purana, one of the eighteen Mahapuranas, mentions that during the battle between Banasura and Lord Krishna, Lord Shiva advised the demon Banasura to worship his son Lord Ganesha before commencing battle against Krishna. Thus the asura praised and adored the elephant-faced lord and then went to the battlefield. Ganesha was pleased with his adoration and blessed him.
The right side and the left side of Banasura were protected by Lord Kartikeya (Skanda) and the he was shielded from his back by Nandi, the divine bull of Shiva and Bhairava Rudra.
