extra-
sensory
perception
(ESP)
ESP has basically three components to it:

telepathy
  Literally, "distance feeling." The term is often a shortened version of mental telepathy and refers to mind- reading, discerning another's thoughts through esp.

clairvoyance
An alleged extrasensory ability to see things beyond the range of the power of vision.

precognition   Psychic knowledge of something in advance of its occurrence.
Certainly there are many claims as to the reality of such powers, but there is far from any absolute proof that the powers of esp actually exist.  Parapsychologists the world over are constantly at work in an effort to prove the many claims of certain persons that claim to possess these powers.
Still, claiming that such powers exist and proving beyond a doubt that they indeed do are like the difference between night and day.  Merely believing these things exist, again, does not cut it; it must be proven.  That is how science works and the burden of proof is on the ones that claim such powers are indeed real. 
For further reading check out these links.
New Analyses Raise Doubts About Replicability of ESP Findings
The Telepathic Terrier
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