Water running in basement floor drain but no faucets or toilets are running
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.