The earliest experiment to demonstrate superposition was done as far back as 1803,long before the concept of superposition.

Thomas Young experimented with light.  He showed that if you shoot light at a barrier with two small slits close together, the light interferes with itself, causing a pattern on the other side.  From this Young concluded that light must be a wave, rather than a particle, since it resembled the pattern you get from waves colliding.  If it were a particle, it would make two spots of light, rather than alternating bands of light and dark.

But Einstein showed in 1905 that light was also a particule.  He showed this through the photoelectric effect: light only knocks electrons out of metal when it has a certain amount of energy.  From this, he concluded that light was particles.

It later turned out that Young's interference pattern appeared even when you used only a single photon at a time.  That's where the explanation of superposition comes from: the single photon is a superposition going through both the left and right slits and interfering with itself.  That's how the photon gets to be both a particle and a wave.

The principle of superposition has since been demonstrated with electrons and even whole atoms. 
Source(s):
http://www.sciencemag.org/cgi/content/abstract/325/5937/174
http://abyss.uoregon.edu/~js/21st_century_science/lectures/lec13.html

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