Why does the sea water look blue?

Clear sea water is intrinsically blue.* The thicker the observed sample is, the bluer it looks. In smaller water basins, like tap water bath's and Swimming Pools, water appears colorless.

* Related Information:

The blue color is caused by selective absorption of infrared spectrum of the sun light.

Water doesn't derive its color from the blue sky. However, without sunlight water can't be seen as blue.

Impurities dissolved or suspended in water may give water different colored appearances, which is more often the case in sea water and lower lakes (greyish brown) than is ice lakes higher in the mountains (blue).

(cf. Related links for further detailed explanation on 'Why is water blue')

This has nothing to do with the blue sky color:

*The sky appears blue because blue light has a shorter wavelength than green and red light (blue light - 700nm, red light 400nm). Very small molecules in the atmosphere scatter blue light, where as green and red light passes straight through and we do not see it.