The stage magician James Randi has offered a cash prize since 1964 for anyone who can demonstrate a supernatural ability under test conditions. From an initial $1000 of his own money, the pot on offer has now grown to $1 million.
Randi claims that no one has passed the preliminaries. No well-known psychic, on the level of John Edward or Uri Geller, has applied to be tested. A British medium, Patricia Putt, was tested in 2009, and failed. A rare glimpse of Randi in action can be seen in this TV documentary, in which he and Professor Christ French tested Derek Ogilvie, a Scottish medium who claims to achieve telepathic contact with pre-speech infants. Ogilvie failed also.
For the official view about the Million Dollar Challenge's aims and operational details, see the article by Jeff Wagg on the James Randi Educational Forum website. This Wikipedia article contains some background detail.
To understand how misleading the Challenge ultimately is, see this well-researched article by Greg Taylor of The Daily Grail. It was written in 2008 after Randi announced that the Challenge would be withdrawn two years later, although its termination was subsequently rescinded.
A series of pieces in a similarly sceptical vein is by Michael Prescott on his blog.
This tetchy email exchange between Alex Tskaris and James Randi is typical of the way potential applicants are handled. See also this description by an audio buff who tried to apply for the prize.