Telepathy
Telepathy (literally "distant perception/feeling") refers to the supposed ability to communicate information from one mind to another, and is one form of extra-sensory perception or anomalous cognition. This information is generally reported as being "received" in the same form as that from the conventional senses.
Some, for example Spider Robinson in the book Deathkiller, have envisioned neurological research leading to technologically assisted telepathy.
The controversial British academic Professor Kevin Warwick of the University of Reading claims that his research into implanted radio transmitters is the first step towards a kind of telepathy. Others view Warwick as a self-publicist, and regard his claims with extreme skepticism.
Parapsychologists have performed a number of experiments attempting to provide repeatable evidence of the existence of non-technological telepathy. Perhaps the closest they have come is with studies of so-called Ganzfeld phenomena.
Comic books take greater liberties with telepaths, giving them the ability to not only control minds (through hypnosis-like capabilities, illusion, etc..) but actually turning telepathy into an offensive weapon by overloading the mental communication channel with a "mind-blast" which causes great pain, unconsciousness, and sometimes even death.
Additional Resources
Someone else will have to supply the details of the experiments and controversy... :-)