Most believers come by their convictions either through personal experience or anecdotal evidence. If you have a dream that eventually comes true, in strikingly similar detail, you might very well take it as proof that you're psychic. And if you hear enough incredible ESP stories from reliable sources, you may have a harder and harder time discounting the phenomenon.
Undeniably, the world is full of both of these forms of evidence. Most of us encounter extraordinary coincidences now and then, and there are many well-documented cases of apparent precognition and clairvoyance. For example, in 1898, Morgan Robertson published "Futility," a novel about a huge luxury liner called the Titan. The story allegedly came to him in a sort of trance. In the novel, the ship zips through dense fog late one April night, crashes into an iceberg and sinks, killing hundreds of people. Fourteen years later, the Titanic, similar in size and structure to the fictional ship, did exactly this, at the same time of year, under the same conditions. For both the fictional ship and the real ship, the casualties were high because there weren't nearly enough lifeboats on board.
There are dozens of other famous stories, most not as well documented, detailing major and minor examples of apparent ESP all over the world. But as compelling as these stories may be to believers, they're of limited use to scientists because they occur in an uncontrolled environment. In order to effectively demonstrate something with hard evidence, scientists need to conduct structured laboratory experiments with closely controlled conditions.
Since the 1930s, parapsychologists around the world have been doing just that. J.B. Rhine, often dubbed the father of parapsychology, was behind one of the earliest and most famous efforts, the Zener cards experiments. The original Zener cards (named after their designer, Karl Zener) were a deck of 25 plain white cards, each printed with one of five simple, distinct patterns. Each deck contained five cards of each pattern, so anybody had a one-in-five chance of correctly guessing the pattern on any particular card.
The experiment was simple: Rhine would ask his subject to guess which pattern was on each card and record the result. On average, random guessing would yield five "hits" (correct guesses) per deck of 25. Rhine reasoned that consistent accuracy above that level, barring any cheating, indicated ESP ability.
The scientific community was certainly surprised, and largely incredulous, when Rhine claimed in his treatise, "Extra-Sensory Perception," that some of his subjects consistently guessed correctly above chance levels. Many disputed Rhine's methods and his credibility, but in general, he was regarded as a legitimate, sincere scientist.
In the years since Rhine's pioneering work, hundreds of parapsychologists have conducted similar experiments, sometimes with the same positive results. Most of these researchers have moved away from the rigid patterns of Zener cards to more open-ended images, such as paintings or photographs. In a typical experiment, a "sender" will concentrate on a particular image (a target) and try to communicate it telepathically to an isolated subject. The "receiver" subject describes what he sees in his mind, and the research team records his impressions. At the end of the session, the receiver attempts to pick the correct target out of a collection of images created from his impressions during the session.
In ganzfeld (German for "whole field") target experiments, developed in the 1970s, the receiver is deprived of sensory information to make it easier to focus on ESP messages. The subject lies in a room filled with dim red light, listening to white noise, with his or her eyes covered (by halved Ping-Pong balls in the conventional experiment). Most of the time, receivers in these experiments are way off in their guesses, but some subjects do describe the target images in striking detail. There are several examples of impressive hits at PSI Explorer: The Ganzfeld Experiment. In similar experiments, designed to test clairvoyance alone and not telepathy, there is no sender, only a receiver.
In another popular experiment, subjects attempt to influence a machine, such as a random number generator, with their minds. Over the course of hundreds of runs, researchers have found that subjects do appear to have some influence over machine behavior, though it is very slight. Check out Princeton's Engineering Anomalies Research department Web site for more information.