Telekinesis, The ability to move objects without contact or other physical means.

Psychokinesis, The ability to move physical objects without using physical means, as with one's mind. One can also consider psychokinesis a larger scope of influences, rather then just motion. For example, mentally affecting the output of a random number generator, or make objects explode.

Telepathy, The idea of being able to communicate with other people/things without sound, visual, or other cues. The ability to allow experiences, knowledge and emotions to be shared between people, without the need to resort to a crude method of communications, such as words.

Precognition, previous cognition : the ability to sense the probable future or destined future. Precognition is the scientific term of this phenomenon; in other contexts, sensing the future might be known as prophecy, the art of divination, or fortunetelling.

Prophecy, A prophecy is a prediction or preconception of an event, usually of religious nature spoken by prophets and false prophets : A declaration of something to come; a foretelling; a prediction; esp., an inspired foretelling.

Some methods of the "art of divination":
Tarot cards - divination from playing a specific set of cards.
Runes - divination from playing a set of marked stones.
Astrology - divination through observation of constellations and other celestial bodies.
Ouija board
I Ching
Numerology
Aeromancy / Austromancy - Divination from the state of the atmosphere and winds; forecasting changes in the weather.
Alectryomancy / Alectoromancy - Divination from a rooster and corn.
Aleuromancy - Divination by flour.
Alomancy - Divination by salt.
Al-phitomancy - Divination by barley meal.
Aquamancy - Divination by water.
Bibliomancy - lines or passages from the Bible.
Cartomancy - Fortune telling with the aid of cards.
Chartomancy - Divination by paper cards and charts.
Cleromancy - throwing small objects. Dates back to ancient Greece and Rome.
Cephaleonomancy - divination by the broiled head of a donkey.
Cromniomancy - divination by onion.
Daphnomancy - a form of Pyromancy with a laurel branch.
Geomancy - divination from figures or lines.
Ichthyomancy - divination from the heads and guts of fish.
Necromancy - divination from spirits of the dead.
Ornithomancy - divination from the flight of birds.
Pessomancy - divination from pebbles or beans.
Pneumancy - divination by blowing out candles.
Psychomantium - an ancient form of divination by mirror-gazing.
Pyromancy - divination by fire.
Rhapsodomancy - divination by means of verses.
Stichomancy - lines or passages from a book.
Sphexomancy - divination by means of wasps.