When Einstein started to think about gravitation, he completely created a new theory that no experiment supported. He based his reasoning, as he explained it later, on small thought experiments (Gedankenexperiment) that led him to formulate the equivalence principle. From this equivalence principle, he used the principles of physics and understood that a new space-time geometry was necessary and after years of effort he obtained the Einstein's equation. It is only when he used this equation to compute the anomalous perihelion advance of the planet Mercury that he knew his theory had something to do with the real world (but one could not call this a prediction). Since then, many predictions of General Relativity have been successfully checked experimentally.
A thought experiment is an experiment that has not been realized, but that was imagined. The results of such experiment are based on well established physical principles but have never been observed physically. A second example of a thought experiment considers a frictionless movement of a vehicle on a road (see Einstein and Infeld, The Evolution of Physics: The Growth of Ideas From Early Concepts to Relativity and Quanta, chapter 1 on the Galilean relativity). Another example in particle physcis is described in one of the above comments. Thought experiments only draw conclusions from physical considerations, not from mathematical derivations, and can therefore be used as illustrations destined to non-physicists.
Does anyone think of other thought experiments which results have been proved relevant later by physical experiments, either because the thought experiment has been realized or because its results had physically testable consequences ?