Stories of the origin of Lord Ganesh

In the puranic tradition there are numerous stories about the manifestation of Ganesh. Each story may seem entertaining but there is a lot of symbolism hidden within each such tale.
The most commonly known story of the origin of Lord Ganesh is taken from the Shiva Puran and goes like this:

Mother Parvati was taking a bath. The Shiv Ganas were guarding the garden and palace where she took her bath. She had instructed them not to allow anyone to come in. Her husband and the lord of the Ganas, Lord Shiv wanted to meet her. He walked into her bath house. Mother Parvati was very embarrassed to see her husband standing there while she bathed. Her attendants complained that this happened only due to the fact that they did not have their own guards. Mother Parvati took some clay and made a beautiful boy, breathed in life into it. She then told the boy that he was her son and should guard the palace and none must enter without her permission. It so happened that again Lord Shiv appeared and wanted to meet the divine mother Parvati. The boy would not let him in saying that he was instructed by the divine mother not to let anyone in as she was bathing. Lord Shiv tried to reason with him but he would not listen. Eventually a battle ensued and Lord Shiv chopped of the boy’s head. In the meantime Mother Parvati had finished her bath. As she stepped out she was horrified to find her son dead and started weeping. Lord Shiva to please her promised to make him alive again. He sent all his ganas(attendants) to look for the head but it was nowhere to be found. Lord Shiv then asked them to bring the head of the first living being they found. This happened to be an elephant. Lord Shiva put the head of the elephant on the boy and made him alive again. Mother Parvati became overjoyed. All the Devis and Devtas blessed the boy and conferred on him the boon that without his presence and worship first, no prayer would be effective.

A story from the Padma Puran
Once upon a time the Goddess mother Parvati was taking a bath. Before she took a bath she smeared her body with various herbal oils and pastes. When she took of all this paste she playfully made a sculpture of the human with the elephant head. While bathing she then immersed the statue into the Divine ganges. The Divine mother Ganga considered mother Parvati as her friend, so she filled the statue with prana (life) and the small toy converted into a huge human form. The Divine mother Parvati called him a son. All the other Devis and Devtas called him Gangay as he had arisen from the river Ganga.
Lord Brahma made him the leader of all the Ganas that is the Devis and Devtas. So he came to be worshiped first among all Devis and Devtas.

A Story from the Linga Puran
Once upon a time the demons, by worshipping lords Brahma, Vishnu and Shiva became very powerful. So powerful they became that they disturbed the gods by creating obstacles and difficulties for them, all the time. The gods were tired of being harassed by demons and prayed to Lord Shiv to grant them a power that would create obstacles and difficulties for the demons and not allow them to enter the region of heaven. Lord Shiv bestowed them this boon. After some time Lord Ganesh appeared at Mount Kailash and mother Parvati accepted him as her son. She empowered him to create obstacles for anybody who would attempt to enter the region of heaven without proper and Vedic worship. So god Ganesh creates obstacles for all those who follow the demonic ways. But by praying to Lord Ganesh the reverse happens, all obstacles are removed.