The oil drop experiment was an experiment  performed by Robert Millikan and Harvey Fletcher in 1909 to measure the elementary electric charge (the charge of the electron).

The experiment entailed balancing the downward gravitational force with the upward buoyant and electric forces on tiny charged droplets of oil suspended between two metal electrodes. Since the density of the oil was known, the droplets' masses, and therefore their gravitational and buoyant forces, could be determined from their observed radii. Using a known electric field, Millikan and Fletcher could determine the charge on oil droplets in mechanical equilibrium. By repeating the experiment for many droplets, they confirmed that the charges were all multiples of some fundamental value, and calculated it to be 1.5924(17)10?19 C, within one percent of the currently accepted value of 1.602176487(40)10?19 C. They proposed that this was the charge of a single electron.

[b]Background[/b]
Starting in 1900, while a professor  at the University of Chicago, Millikan, with the significant input of Fletcher[1], and after improving his setup, published his seminal study in 1913.[2]

His experiment measured the force on tiny charged droplets of oil suspended against gravity between two metal electrodes. Knowing the electric field, the charge on the droplet was determined. Repeating the experiment for many droplets, Millikan showed that the results could be explained as integer multiples of a common value (1.59210?19 C), the charge on a single electron.

At the time of Millikan and Fletcher's oil drop experiments, the existence of subatomic particles was not universally accepted. Experimenting with cathode rays in 1897, J. J. Thomson had discovered negatively charged "corpuscles", as he called them, with a mass about 1000 times smaller than that of a hydrogen atom. Similar results had been found by George FitzGerald and Walter Kaufmann. Most of what was then known about electricity and magnetism, however, could be explained on the basis that charge is a continuous variable; in much the same way that many of the properties of light can be explained by treating it as a continuous wave rather than as a stream of photons.

The so-called elementary charge e is one of the fundamental physical constants and its accurate value is of great importance. In 1923, Millikan won the Nobel Prize in physics in part because of this experiment.

Aside from the measurement, the beauty of the oil drop experiment is that it is a simple, elegant hands-on demonstration that charge is actually quantized. Thomas Edison, who had previously thought of charge as a continuous variable, became convinced after working with Millikan and Fletcher's apparatus. This experiment has since been repeated by generations of physics students, although it is rather expensive and difficult to do properly.
Data and images from  http://en.wikipedia.org/wiki/Oil_drop_experiment
[img]http://www.phy.ntnu.edu.tw/ntnujava/index.php?action=dlattach;topic=1913.0;attach=3276[/img]