Psychic (Fallout)

After being dipped in FEV vats, absorbing some other people and being connected to the LA Vault computer, the Master gained some psychic powers the extent of which is unknown. He was able to attack humans mentally, although his attacks could be repelled with proper training.

The Master was able to somehow bring forth psychic abilities in certain humans after they were injected with FEV, but most of the experiments were failures (resulting in insanity) or used to line the corridor of revulsion. There were four psykers in the Master's lair: Wiggum was electrokinetic-dominant, Lucy was telekinetic-dominant and a minor photokinetic, Moore was pyrokinetic-dominant, and Gideon was a receiving-telepathic-dominant (without the ability to control his telepathy, requiring the psychic nullifier to block incoming thoughts) with minor photokinetic abilities. All four of them died when the Cathedral was vaporized in nuclear fire.

Hakunin, the Arroyo shaman, apparently also possessed some telepathic abilities, as he was able to speak to Chosen One in his dreams.

A group of tribals known as the Beastlords had a kind of psychic control over animals.

SPECIAL
The ability to resist the Master's psychic attacks is represented in the SPECIAL system by the Mental Block perk.

Appearances in games
Some kind of psychic powers appears in every Fallout game, although Chris Avellone would prefer for it to be gone from the setting, as stated in Fallout Bible 3. Avellone says:
 * For Fallout fan-fiction purposes, you are welcome to make use of the psykers and their potential from Fallout 1, but I'd be careful - the psykers in Fallout 1 show some pretty over-the-top mutations that could take the world to Childhood's End faster than you can say "uh, his eyes are glowing?"