Whenever we turn on a shower or fawcett shortly after it is turned off we hear several seconds of water running in the pipes.recently we have started to hear the water run even without turning on a sink or shower. Any ideas on what I should check into

You have a leak somewhere in the walls. You'll find it as soon as the water starts ruining your floors or better yet ruins the ceiling below where the leak is. Hearing leaks spells trouble and they need to be investigated before they get out of hand.

Do you have PVC drain pipes, the white plastic drains? When you say you hear water running do you mean the sound of a supply pipe or a drain pipe?