While some foreign equivalents of the penny can float on water, the American penny will not float on water. The American penny is over 97 percent zinc and just over 2 percent copper. Zinc has a density of 7.14 gram per centimeter cubed, compared to water, which has a density of about 1 gram per centimeter cubed.
As a general rule, a denser object will sink in a less dense liquid. The exception is when the surface tension of a liquid can overcome the force of gravity of the dense object. Due to the large difference in density between the American penny and water, the surface tension is not sufficient to keep a coin afloat.