Ganesha is known to be the Siddhi Data - one who bestows the Siddhis to the eligible aspirants. In the Tantric traditions the eight Siddhis are considered as goddesses who are the consorts of Ganesha.
The Ganesha Purana also mentions that he killed a demondemons with the help of these Siddhis that he possesses.
Quoting from the book "Essence of Ganesha Mahima" (hosted at Kamakoti.org):
Ganesha’s wedding : Some devotees of Ganesha presume that He was a bachelor but others feel that his life partners would have to match up with his own Maha Devi Swarupa’s magnificence.But keeping in view of His presence with a peculiar physical features and as he continued to be a bachelor, he was angry and upset and even Deva ganas- let alone human beings, were troubled at the wedding ceremonies by sending groups to mice at the wedding functions and creating problems at the eateries and wedding party residents. Groups of Devas appealed to Brahma Deva and the latter had to seek a solution. This was how, He had to create two ‘kanyas’.According to Shiva Purana, both Ganesha and Skanda Kumara were desirous of Prajapati’s daughters Siddhi and Buddhi and Ganesha had won and Siddhi begot Kshema or Prosperity / Shubha or auspiciousness and Laabha or Profit to Budhi. In any case, whenever Ganesha is present, siddhi 'success' and buddhi 'wisdom' are not far behind. Ganesha's relationship with the Ashtasiddhis or the eight spiritual attaintments obtained by the practice of yoga are the eight glorious powers are represented by a group of young women who surround Ganesha. In the Shakta worship of Ganesha, the Ashta Siddhis are addressed as eight goddesses. In Ganesha Purana, these personified Ashta Siddhis are used by Ganesha to attack demons viz. ‘Devantakas’ are known as Anima: to reduce one's body even to the size of an atom; Mahima or to expand body in sizes infinite; Garima; Laghima or becoming weightless; Prapti or possessing unrestricted access to any place in the world; Prakamya or fulfillment of any wish ; Ishitva or possessing absolute Lordship and Vashitva or to subjugate all.]