Some of the largest users of kerosene are the airlines. Jet airliners are fueled with it and it takes a lot of fuel for one of these large airplanes. The fuel is used quickly. As a safety precaution, the fuel tanks are sumped daily. What that means is that a few gallons of fuel is wasted every day because it may have water in it.
Fortunately, the water drops to the bottom. The specific gravity of kerosene is lighter than water and so water drops and kerosene floats. This is why sumping out the bottom of the tank will get rid of the water.
Due to temperature changes (causing expansion and contraction), condensation will occur on fuel that has been stored for a lengthy period of time. To be safe, follow the same precautions as the airline. Use the fuel on top and then sump out the fuel at the bottom that may have water in it.
Water will clog up the wick so that the capillary action does not work. This is the worst case. Smaller amounts of water can make a hissing or crackling sound and make the flame dance around. Water in the kerosene will cause the wick to develop tar more quickly.
A wet wick does not have to be thrown away. Instead, you can take the wick out and dry it with paper towels and evaporation.
If you have too much water, in your stove or heater, you should take the tank out, if possible, and rinse it with high grade k-1 kerosene. Then, you should wipe down the appliance with a cloth. Finally, take out the wick and dry it out.