Please accept my humble obeisance. All glories to Srila Prabhupada
Following are some types of sidhhis:
(1)The ability to know all languages including those of animals: In Valmiki Ramayana, Kishkinda Khanda, sarga 56, Angada speaks about Jatayu’s death and Sampaati bird hears his brother’s name and asks the Vanaras to narrate more. The vanaras narrate about Jatayu.
(2) Knowledge of one’s past lives: In SB.5.12, Jada Bharata explains his past life to king Ragugana.
(3) Knowledge of the nature of other people’s minds
(4) The ability to make one’s body invisible: In Valmiki Ramayana, Yuddha kanda, sarga 80, Indrajit, the son of Ravana made himself invisible while fighting. Also in Valmiki Ramayana, Yuddha kanda, sarga 74, after having been struck by Brahma’s missile released by Indrajit, Rama and Lakshmana became unconscious. Sixty-seven crores of monkeys fainted. Hanuman and Vibhishana, however in consciousness, roared about in the battle-front with torches in their hands, making a search of Jambavan. They find Jambavan. Jambavan requests Hanuman to proceed to Himalayas, by crossing over the ocean and to bring four important herbs, viz. Mrita Sanjivani, Vishalya karani, Suvarna karani and Sandhani; so as to bring succor to the fainted army of monkeys. Hanuman begins his journey to Himalayas and reaches Mount Rishabha, where the wonderful herbs exist. Hanuman searches for the four wonderful herbs. The herbs made themselves invisible hearing the sound of someone in the mountain.
(5) The ability to make the sounds of one’s body not hearable: In Ramayana while entering Lanka Hanuman used this power.
(6) The ability to make everyone happy and joyful: Devotees like Hanuman always make everyone happy and joyful even just by their presence (Ref. Ramayana).
(7) The ability to possess great strength: In Ramayana, we come to know about many great personalities like Jambavan, Sugriva, Vali, Ravana, Angada, Hanuman, and so on who possessed great strength.
(8) The ability to locate hidden things: In Valmiki Ramayana, Sundara kanda, sarga 15, Hanuman met Sita Mata who was kept hidden by Ravana.
(9) The knowledge of the fourteen planetary systems,
(10) The knowledge of the arrangements of stars,
(11) The knowledge of the movement of stars and
(12) The knowledge of bodily anatomy: The Sapta Rishis possess all the knowledge and they keep changing according to manvantras (the duration of manus). The Sapta rishis of this current Vaivasvata (seventh) manvantra are : Atri, Bhrigu, Kutsa, Vasishta, Gautama, Kashyapa and Angirasa(refer : Jaiminiya Brahmana.2.218-221; Brihadaranyaka Upanisad2.2.6; Gopatha Brahmana 1.2.8; Mahabharata; Brihat Samhita).
(13) The ability to remain motionless: In Valmiki Ramayana, Sundara kanda, sarga 48, Ravana calls Indrajit and asks him to go for a battle against Hanuman. Indrajit wielding a colourful bow quickly in a chariot to face Hanuman in combat. The arrows discharged by Indrajit are made ineffective by Hanuman, through his peculiar skill of maneuvering them like a wind-god. Realizing that Hanuman cannot be slain, Indrajit merely takes him captive by discharging the unfailing missile presided over by Brahma, the creator. Hanuman falls on the ground motionless to honour the missile because it was presided by Brahma, the creator. The demons tie him with ropes and drag him to the presence of Ravana. Hanuman yields to their operation of capture, even though capable of aborting it, eager as he was to meet Ravana.
(14) The ability to perceive the celestial beings: In Mahabharata, the Pandavas possessed great powers and had this ability too.
(15) The understanding of consciousness and
(16) The knowledge of the soul: Many self-realized persons like Janaka Maharaja possessed the understanding of consciousness and the knowledge of the soul (refer à Ramayana).
(17) The ability to walk on water, thorns and similar objects: By yogic perfection one can possess this ability(Patanjali yoga-sutra, chapter IV).
(18) The ability to surround oneself with a blaze of light
(19) The ability to be omnipotent and omniscient: In Ramayana and Mahabharata there are many great personalities like Lakshmana, Bharata and so on who had this ability.
Lord Ganesha possesses all the siddhis and riddhi and Hanuman possesses all the siddhis,riddhi and nava-nidhis.
Srila Prabhupada has taught us to avoid pursuing these siddhis. In this age of Kaliyuga - the best form of purification is chanting of the holy name of Krishna. If Krishna is satisfied there is no need to attain any siddhis.