I can see/hear water running through the pipe just under the basement floor drain in the laundry, furnace and hot water heater room. Nothing is turned on in the house. If I turn off the main water inlet to the house, the water in the above mentioned pipe stops after a minute or so. No leaks in toilets or faucets. What could be causing this?
in some older homes, the sanitary sewer and stormwater drain lines are tied into one line out to the street mains. you could be hearing/seeing drainage water from your exterior foundation weeping tiles draining into the main drain. its often set up so that the basement floor drain acts as a vent, overflow and inspection point just upstream of where it dumps into the gas trap at the entry to the sanitary sewer portion of your household drain.
you can also look for a small plastic line that runs from somewhere just after the main shutoff down into the concrete floor. this small line is designed to constantly flood water into the floor drain to ensure there is always water in the subslab trap at the aforementioned spot. this ensures you dont get a dry trap and get methane coming up into the basement from the floor drain.
Watch your water meter. For example, check the meter before leaving the house for the workday or something and make sure that all water sources are turned off and nobody uses water for anything, then when you get back home check the meter again.
If the number is different, then you probably have a water leak. If you know that all water sources are turned off, then the meter should not have changed at all.
If the number is the same, but you still see/hear water in the drain, then maybe it's one of the things pointed out in the other answer.