Psychokinesis

Psychokinesis, or telekinesis, is the ability to move objects with the power of the mind without applying any evident physical force.

After unshielded exposure to the barrier at the edge of the galaxy, Gary Mitchell developed this ability, among others. Evidence obtained from the Valiant's recorder-marker suggested that at least one individual in that crew developed the same or similar capabilities. 

The Platonians acquired the ability after settling on Platonius, thanks to an unusual substance named kironide. Because kironide must be processed by the pituitary gland, individuals with glandular defects, like Alexander, could not process the substance and therefore did not develop the power. 

The mute humanoid known as Gem, in addition to being an empath, was able to induce physical healing in other lifeforms, at the cost of causing similar damage to herself. 

Vulcans in the monasteries of Mount Seleya may possess this ability. One example is when Captain Spock's body was brought for the Fal-tor-pan ritual, priestesses carried his body by holding their hands above him (assuming that no anti-gravity technology was being used). 

The remote Federation outpost Darwin Genetic Research Station on Gagarin IV experimented in genetic engineering, which included making all of their "children" telekinetic, as well as telepathic. Trapped in an observation bay, the "children" (who appeared to be in their early 20s) would play three-dimensional chess with their telekinesis. 

Some Vorta also have this ability, such as Eris. 

Centuries ago, the Ocampa naturally had this power, but after years of care from the Caretaker it fell into disuse. A group of them that left learned this ability from Suspiria. 

Just before leaving the starship USS Voyager, Kes' powers had advanced so much her telekinesis activated without her even trying, such as when The Doctor asked for a hypospray it flew across the room to her. 

Psychonkinetic races or beings

 * Anaphasic lifeforms
 * Armus
 * Charlie Evans
 * Companion
 * Douwd
 * Humans (genetically enhanced (Gagarin IV members) or biologically compromised (Gary Mitchell and the Galactic Barrier))
 * Gary Mitchell
 * Gem
 * Nacenes
 * Pah-wraiths
 * Prophets
 * Ocampa (most lost)
 * Q
 * Thasians
 * Trelane
 * Vorta (some)
 * Zalkonians (some)

Apocrypha
According to the novel The Battle of Betazed, some hidden mental teachings are able to unlock the ability of telekinesis in Betazoids.