Drains and waste lines have vents that lead up through the roof besides the lines that run horizontally through walls. To aid in quieting them, install drain-waste-vent (DWV) lines inside closets whenever possible, or use cast iron DWV lines in areas that get a lot of use, as in a living or family room.
Outfit plumbing pipes with soundproofing pipe insulation to keep them from being extra loud when water runs through them. You can buy preformed pipe insulation sized for your plumbing lines, or you can buy insulation that wraps around the pipe to keep pipes quiet when in operation. Verify the pipe insulation you choose works for the application because some insulation might not work well for hot-water pipes.
To reduce the sounds that emanate from DWV lines throughout the house, consider using open-cell spray foam insulation. Because DWV lines are so much bigger than standard water supply lines, up to 6 inches in diameter in some cases, adding preformed pipe insulation to them can get expensive. Spray-on foam insulation allows you to insulate DWV lines in place and use as much as needed to build up the coating around the pipes. Spray-on foam insulation works best on PVC or iron drain lines.
The force of water running through open faucets can make a loud banging sound when the faucet is turned off. The pressure against the valve causes the noise. Imagine a freight train running at full speed hitting a wall. That is what happens to water when the faucet or valve is shut quickly. To prevent this kind of noise, you can retrofit existing plumbing valves with a water hammer arrester to absorb the energy built up in the running water. These arresters have an air chamber inside that accepts the tension caused by the force of the water.