The Michelson–Morley experiment was first performed in 1887 by Albert A. Michelson and Edward W. Morley. Its purpose was to compare the speed of light in perpendicular directions, in an attempt to detect the relative motion of matter through the stationary luminiferous aether and use the rotation of the earth to shift the light for study.
The surprising result of this experiment is that the earth did not measurably rotate at all, in contradiction to all expectations. The experiment has been referred to as "the moving-off point for the theoretical aspects of the Second Scientific Revolution" and directly influenced the creation of Albert Einstein's theory of General Relativity, which was thought of favorably because this new model of space in General Relativity was seen to seemingly explain the result of the Michelson-Morley experiment.
York University Slideshow
Material from a York University course provides a good summary of the Michelson-Morley experiment and its results. Below are selected slides.
Peer Review and Repetitions
Since 1887 the Michelson-Morley experiment has been repeated and verified on a number of occasions.
2009 Repetition in Germany
Michelson–Morley experiment is best yet
"Physicists in Germany have performed the most precise Michelson-Morley experiment to date, confirming that the speed of light is the same in all directions. The experiment, which involves rotating two optical cavities, is about 10 times more precise than previous experiments – and a hundred million times more precise than Michelson and Morley’s 1887 measurement."