Just to put a bit more science behind what Jim and Terry are saying.
Water, like any other matter, possesses momentum when it's moving. Turn off a valve, and that column of still-moving water in the pipe has nowhere to go except to slam into the closed valve. The quicker the valve closes, the faster the water is still moving at the moment of zero flow. This creates a high pressure spike, which travels backward through the pipe at the speed of sound, and can blow out joints and fittings, or soft spots in pipe walls, if it's already getting weak. This can happen anywhere in the system, not just right next to the source of the hammering. If there is a small leak already, much of the pressure escapes there. If not, the pipe itself must absorb the energy, by recoiling and slamming against a nearby wall. That's your thud.
Having the pipes perfectly secured to the wall can eliminate the thud, and I've heard a few licensed plumbers working shifts at HD advocate this as the solution to hammering, but it does nothing to suppress the pressure wave itself, so the eventual blowout risk is still there.
A hammer arrester is just an air chamber with a piston inside, so the air and water never touch. Place one right next to the quick-closing valve that causes the hammering, the air cushion absorbs the momentum, and the pressure spike is prevented altogether. Place one anywhere else, and it protects whatever is nearby from the effects of a pressure spike that starts elsewhere.
+1 to arresters on the WM (and DW) being a good idea. I'd put one on the toilet, too, even if the new valve has helped.
+1 to checking your incoming pressure as well. If it's high, that means the hammering is that much more powerful and more likely to cause damage at some point down the road. You'll just need a lazy hand pressure gauge. Set it somewhere and leave it overnight.