Toilets, Sinks, Showers, Tubs and Disposals - Another running toilet question

I did a search, but everyone seems to abandon their posts and not reiterate if something worked or didn't. Here's my problem...

After I flush the toilet everything works fine and the filler valve shuts off, but it seems that water is still entering the tank somehow. You can hear the water running and slowly water begins to creep up and over the overflow tube and into the bowl. The only way to stop it is to shut off the water supply.

Where could the water be entering the tank?

You need to replace the toilet fill valve. The valve seat is either worn out or has trash in it. It is not closing completely.

I'd recommend a Fluidmaster. Cost <$10, takes <30 minutes.

Thanks Rick. Could you point out what you mean by "valve seat" in this instruction from fluidmaster? http://www.fluidmaster.com/pdf/400a_instructions.pdf

I assume you mean some part of the fill valve, but I'm not sure which would be leaking.

The valve seat is located at the top of the valve. See item 12 on your site. It shows clearing that area of sand, etc. What happens is sand and other debris gets in the system and tends to stay in the valve area and causes it to wear or pit.
Replacing the entire valve is too quick, cheap and easy. Don't worry with trying to fix the diaphragm.