Generally speaking, you want some air in the lines. That air is usually found in the surge arrestors in high points in the water system. They act like mini shock absorbers for your water system and prevent water hammers(shock waves) in your system. Sometimes these arrestors fail to function in older houses after they become clogged with scale or other debris. Water hammers require water to be moving and then stopped very quickly and sound like someone kicking one of the pipes so I don’t think this is the source of the noise you describe.
Most of the times people want to get some air back into the system. To do this shut off the main water supply to the house, open the highest faucet in the house(upstairs bathroom, etc.), and then open the lowest faucet and allow the system to drain mostly empty. Now close the lowest faucet and turn on the main water supply and let it run until you get straight water out of the faucet in the upstairs. This will recharge all your arrestors.(you will still get air ‘burps’ out of the system for about a day but it won’t hurt anything.)
Thermal expansion and contraction has already been covered and would be my first guess but again, you need fluid moving through pipes at a different temperature to get this effect.
Another possibility is regular buildup of scale and debris in the piping that causes a narrowing or necking down of the pipe. This would sound more like a whistling or thrumming sound and requires moving water. Aside from being annoying this also causes turbulent flow around the obstruction and can result in eddies that cause pitting of the piping adding more turbulence and eventual pinhole leaks in the piping.
A long shot possibility is if you have a keep warm pump on your water system that will cycle on to keep warm water throughout the loop in the house. Very few people have a system like this installed but I have seen it. At least this would give you the flowing water to perhaps cause one of the above situations. Bottom line is I don’t know what is causing your noises but I wish you good luck in figuring it out. If you do find out please let us know. I would be interested in finding out.