Why does wet skin sunburn faster? There is a popular belief that wet skin burns or tans faster. However, I've never heard a believable explanation of why this happens.
The best explanation I've heard is that the water droplets on the skin act as a lens, focusing the sunlight onto your skin. I don't see how this would affect an overall burn, because the amount of sunlight reaching the skin is the same (ignoring reflection).
Is this 'fact' true, and if so, what causes it?
 A: 
Consider these facts: [cdc.gov]
  
  
*
  
*Grass reflects from 2.5 to 3 percent of UV rays hitting its surface.
  
*Sand reflects 20 to 30 percent of UV rays.
  
*Snow and ice can reflect 80 to 90 percent of UV rays.
  
*Depending on the angle of reflection, water can reflect up to a full 100 percent of UV rays striking the surface.
  

As such, one explanation might be:

Most UV rays from the sun (which cause tans and sunburns) can 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.

A: I don't know of any research to find out if skin sunburns faster when wet, though someone did a comparable experiment to find out if plants can be burnt by sunlight focussed through drops of water after the plants have been watered.
You need to be clear what is being measured here. The total amount of sunlight hitting you, and a plant, is unaffected by whether you're wet or not. The question is whether water droplets can focus the sunlight onto intense patches causing small local burns.
The answer is that under most circumstances water droplets do not cause burning because unless the contact angle is very high they do not focus the sunlight onto the skin. Burning (of the plants) could happen if the droplets were held above the leaf surface by hairs, or when the water droplets were replaced by glass spheres (with an effective contact angle of 180º).
My observation of water droplets on my own skin is that the contact angles are less than 90º, so from the plant experiments these droplets would not cause local burning. The answer to your question is (probably) that wet skin does not burn faster. I would agree with Will that the cooling effect of water on the skin may make you unaware that you're being burnt, and this may lead to the common belief that wet skin accelerates burning.
A: 
I'm no expert in biology, and biology may describe this phenomena? I am applying what I know about physics.

Sunburn is caused by excessive exposure to skin-damaging UV light.
I tend to believe that wet skin by itself does not cause you to burn faster, one merely feels cool in water, so one is prepared to stay out in the sun longer. I can't see any reason for why wet skin would amplify the effect of burning (barring localized droplets, possibly causing what I will call "spotted sunburn"). In fact, some frequencies of UV are absorbed by water, which would seem to reduce the effect (by how much, I'm not sure). In fact, having a layer of water on your skin would seem to help reduce sunburn (however slightly) because some of the UV will be reflected by the water.

That being said, consider a large body of water. Here are a couple of situations you might find yourself in:
If you have your body submerged in water it is possible that more UV could strike your skin due to the water surface not being flat (a lensing effect). 
If you are above the water (for example, on a boat, or just your head and shoulders poking out of the water, etc.) there will definitely be more UV striking your skin, due to there being not only direct light from the sun, but reflected light from the surface of the water.

A: The reflectance off water is only about 2%, so about 98% of the solar rays pass into the water layer on your skin, and the bottom surface of that water is optically contacting your skin, so the water acts as an anti reflection coating, that more efficiently couples the rays into your skin layers.
Also a lot of "wet skin" burning, is actually wet tee shirt burning, and the water in the pores of the wet shirt very efficiently couples the rays through to your skin.
A: Well, it doesn't burn faster. I would say it burns slower but tans faster. Thats how dark tan oils work. The melanin absorbs the energy from the sun to charge and store it. The body wants more and produces more melanin. So you would get dark. However I believe the water on the skin just intensifies the energy, not the burning uv ray itself. Therefore, I believe you get darker but do not burn faster. Either slower or perhaps no difference at all. Remember to not look at the sun but keep your eyes open. Only 5% of the necessary sunlight comes through our skin. The rest, through the eyes.
A: Yes. It's is not so much the water is the beach sand reflecting light back to you like a parabolic mirror. The droplets of water on your skin can form more surface area to catch light creating a magnifying effect focusing light on your skin as well. The random texture in the beach sand will also give you even tan. Most sand is white in color even if not the water and sand in its natural state are glossy where dirt or grass absorb more of the spectrum of light including UV light.



