The purpose of Robert Millikan's oil-drop experiment (1909) was to measure the electric charge of the electron. He did this by carefully balancing the gravitational and electric forces on tiny charged droplets of oil suspended between two metal electrodes. Knowing the electric field, the charge on the droplet could be determined. Repeating the experiment for many droplets, it was found that the values measured were always multiples of the same number. This was taken to be the charge on a single electron - 1.602 x 10-19 coulombs (SI unit for electric charge).
In 1923, Millikan won the Nobel Prize for physics in part because of this experiment. This experiment has since been repeated by generations of physics students, although it is rather expensive and difficult to do properly.
A version of the oil drop experment has subsequently been used to search for free quarks (which, if they exist, would have a charge of 1/3 e), without success. Current theories of quarks predict that they are tightly bound and will not exist in a free form.