Do the sun's tanning rays penetrate water and to what degree?

The sun's rays do penetrate water, but each color penetrates to a different extent. Generally, the more energetic colors, those at the upper end of the color spectrum, the blues and violets, penetrate deeper. The lower frequency wavelengths, the oranges and reds, peter out at shallower depths. But these generalities will vary, as the ability of light to penetrate water is affected by what is in that water. Red light is absorbed within 15 to 20 feet, while blue light can make it down as far as 200 feet or more (this is why the deep water appears bluish), depending on the clarity and turbidity of the water.

Snorkelers near the surface need to practice caution because, since UV rays enter the water, they are prone to burn. Wear a t-shirt or dive skin, or wear waterproof sunblock. UV lamps are used to drive reactions and/or sterilize water in municipal water systems. In such systems, if the water is clear, UV-B will travel many centimeters before its intensity is too low to make a significant effect.

Improved Answer:
Most UV rays from the sun (which cause tans and sunburns) reflect off the surface of water. This is actually why so many people get sunburnt while swimming or wading in water -- UV radiation will reflect off the surface of the water onto whatever part of a person is above the water, giving a swimmer or wader a double dose of UV radiation, versus someone far enough inland to not be affected by reflection off the water. The UV reflection is strongest when sunlight's angle to the water is at its lowest, within a few hours of sunrise or a few hours before sunset. By contrast, more UV rays penetrate water and can cause sunburns on completely submerged divers during mid-day, when the sun is high overhead.

as has been said, the suns ray can penetrate water, much will be reflected, in this case the angle of the ray of reflection will be equal to the angle of the ray of incidence (the angle at which the ray of light hits the water), the light that does penetrate will be refracted as it enters the new median in which case the new angle can be found with Snell's law.