My house is now 19 years old, and all 3 toilets started intermittently running! Usually, you just replace the flapper valve, and they stop running. I tried this and it only worked on 1 of the 3 toilets.
To make a long story short, I think what happened on the other 2 toilets, was the rubber gasket material between the flapper seat assembly and the tank got degraded over time. A leak here goes into the bowl, not on the floor, so you do not know where the leak is occurring.
I used to be a plumber for a couple years during my summers in college, and I never ran into an issue like this one before.
I googled it and found no help, beyond change the flapper valve. Once I changed the flapper valve assembly, and made sure I had the bit nut tight enough.......this fixed the other 2 toilets. I decided to make a trouble-shooting chart to help other people if they run into this same problem.