Alan Turing first proposed an "imitation game' as a way to test an entity for the presence of the ability to think - that is intelligence.
The Loebner Prize is an annual competition that puts the Turing Test into practice, held since 1990 - wikipedia 
The Imitation Game
The name he himself gave to what we now call the Turing Test, was the "imitation game".
Alan Turing proposed this Thought Experiment in his seminal 1950 paper Computing Machinery and Intelligence - loebner.net
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It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart front the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A."
We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?" - loebner.net
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Sometimes people have difficulty believing that machines cannot think. Douglas Hofstadter talks about ELIZA, and related issues, his book in Godel, Escher, Bach. pdf
John Searle uses his Chinese Room thought experiment to criticise this in his 1980 paper Minds, Brains and Programs - cogprints.org