Psychic forces, unfettered by superstition and religion, can be very powerful. Some people gain this power by accident. There are many reasons why people become psychic; it might be a result of radiation, genetic engineering, humanity's need to develop and become one consciousness or it might merely be a new face for the same old magic, shaped by urban legends.
Wild Psionics are born, not taught. Their powers are the results of practice and introspection, not by delving into musty tomes or mystic identification with the divine. They do not need props to work their magics, nor do they subscribe to any of the old superstitions.
As described here, psionics is a rather new magic tradition and not yet fully developed. A more mature psionic tradition can be exemplified by The Force and Psionics.
Examples and References
WH40K, comics, anime and manga, movies like Firestarter (1984).
Limitations
Echoes
Psychics are rarely fully in control of their powers. Small abnormal events are common around them, especially when tired. Psychic whispers, involuntary mind reading, poltergeist activity, a visible nimbus or aura. A combination of anxiety, lack of concentration, subconscious urges, and fatigue can cause them to go wildly out of control and even completely take over the psychic, turning her into a creature of mindless impulse.
Geas or Focus
Most psychics have developed some mental crutches that let them concentrate and overcome their anxieties. Unlike a normal geas, the psychic version is never a concrete pronouncement, but instead rather vague; the psychic has some behavior tag that even she may not recognize as the thing keeping her life together.
Sometimes this is not a behavior, but an object, a Focus. This is then often a mundane item, like an old teddy bear, but it can also be a power crystal or technological psi enabler as well as a special costume or a set of props. It can even be a drug or medication. Wild psychers often received their focus item from a mentor as a part of their background.
Loosing this focus item or breaking the geas weakens the psychics powers. Further, it can trigger a rash of extra-powerful echoes, possibly destroying the psychic and endangering the surroundings.
Common Schticks
Rare or prohibited Schticks
Summonables
Only the more powerful and twisted psychics use summoning, but when they do, they bring things into existence from their own subconscious - terrible nightmares out of their own twisted dreams.