When I turn off the water, hot or cold, in any faucet in the house or after the toilets have been flushed there is a loud banging sound. WHY? Please help!!

Hi, we had this problem when we first moved in here, we still don't know what caused it, but what cured it was those tubular foam insulators placed around each pipe in the loft, they are quite cheap to buy and easy to fit. Hope this helps

Lulu's speaking of Armoflex insulation. Whiile this may stop pipes that rattle it's not going to help "water hammer". "Water hammer" happens when you abruptly shut off the water. You have at least 40 pounds of pressure pushing the water flow. The weight of the water hitting a 90 degree bend causes the sound that you hear. We put in shock absorbers,(air chambers) to cushion the hammer much like the shocks on your car.
Back in the 60's we were required to to put shock absorbers,(air chambers) on all bath lavatorys and kitchen sinks. Over time water and condensate built up in them and they must be recharged. First turn off the house at the main house shut off valve. Then open hot and cold faucets at the farthest bathroom to prevent air lock.(This is important.) You will find under each fixture little brass or chrome valves. These are called angle stops. With a small pail held under the angle stop to catch the run off look under the handle of the stop and you will see a nut with the stem running through it. This is called the bonnet packing nut. Put your wrench on it and back it off counterclockwise. Now open the stop and remove the stem and washer assembly, The stop will begain to drain. When it has quit draining reassemble the stop and move on to the next one. Do this on each one of your angle stops. There will be six of them in a two bath home. When you are done, close off the faucets you have opened, turn on the water to the house, and give yourself a pat on the back.
You have just recharged your air chambers and saved yourself a hefty service call bill. Hope this helps you out TOM