Originally Posted by MinConst
Sounds like the flapper. It is sometimes hard to tell that water is coming in. They sell these tablets you can put in the tank and if it shows in the bowl the flapper is bad. Or just replace the flapper and be done with it. It really sounds like that.
Chances are it's the flapper. I replace them a lot for just that same reason.
Another cause might be if the water level is at the top of the overflow tube, it's slowly running down it and the tank has to fill, equally slowly, to refill the tank. The water level should be about an inch below the top of the overflow tube. There's usally a line marked for the maximum fill level. If it's over filling, try adjusting the float. If it still fills to high you have to replace the seal in the fill valve, or just replace the whole fill valve is easy to do and doesn't cost much. But try the flapper first, as that's the more likely cause.