It fell to French physicist Leon Foucault to offer indisputable proof of Earth's rotation. He did so in a novel manner. Realizing that the free fall of a weight was difficult to measure accurately, he began experimenting in his cellar using a 2-meter pendulum with a 5-kilogram bob.
On February 3, 1851 he presented his experiment to his colleagues, and Prince Louis Bonaparte asked him to give a public demonstration. The scene could hardly have been more dramatic. Foucault set up a pendulum more than 60 meters long hanging from the domed ceiling of the Pantheon in Paris. The pendulum never retraced its path as each swing deviated to the right, which meant that the floor of the Pantheon was moving! Foucault had at last provided the first dynamical proof of Earth's rotation. Foucault pendulums now hold a place of honor in science museums worldwide.
The interest in falling bodies did not end with Foucault. In 1902 E. H. Hall at Harvard University conducted a careful experiment in which 948 balls were dropped 23 meters. Using Gauss's theory, he predicted an eastward deviation of 1.8 millimeters. His experimental result was 1.5 millimeters, but he also observed a southward deviation of 0.05 millimeters, which is not expected from Gauss's theory.
As late as the 1940s some authors regarded the southward deviation as a mystery, but it is explicable as part of the Coriolis force. The basic equation predicts only an eastward deviation, but inclusion of further mathematical terms reveals that a small southward deviation should occur. What is amazing is that Robert Hooke expected it more than 300 years ago. High school students seeking a challenging science fair project need look no further!
http://www.lawrencehallofscience.org/gems/rotates.html
Now that we have access to space, the easiest way to prove the Earth is spherical is to leave it and view it from a distance. Astronauts and space probes have done just that. Every picture of Earth ever taken shows only a circular shape, and the only geometric solid which looks like a circle from any direction is a sphere.
One of the oldest proofs of the Earth's shape, however, can be seen from the ground and occurs during every lunar eclipse. The geometry of a lunar eclipse has been known since ancient Greece. When a full Moon occurs in the plane of Earth's orbit, the Moon slowly moves through Earth's shadow. Every time that shadow is seen, its edge is round. Once again, the only solid that always projects a round shadow is a sphere.
http://www.physlink.com/Education/AskExperts/ae535.cfm