Sunlight is made up of all the colors of the rainbow: red, orange, yellow, green, blue, and violet. Some of the sunlight is reflected off the surface of the water, reflecting the color of the sky. Some of the sunlight penetrates the water and is scattered by ripples and particles in the water (this tinges the appearance of the ocean with the color of the particles). In deep water, much of the sunlight is scattered by the oxygen in the water, and this scatters more of the blue light.

Water absorbs more of the red light in sunlight; the water also enhances the scattering of blue light. Sir Chandrasekhar Venkata Raman (an Indian physicist) won the Nobel prize in 1930 for his work on light.


Some Oddly-Colored Seas:
The Red Sea often looks red because of red algae that live in this sea.
The Black Sea looks almost black because it has a high concentration of hydrogen sulfide (which appears black).

Links:
A page on the ocean's color from Charles L. Braun and Sergei N. Smirnov, Dartmouth College
Ocean images from NASA