Where is the water going?
Is the tank full to the overflow?

Is the fill valve not closing properly?

If it has a long are with a float, pull the float upwards gently and see if the valve then closes.

If the running is periodic the flapper may not be sealing correctly and water from the tanks is slowly leaking into the bowl all the time.

The often results in 'phantom flushing.'

The toilet is not actually flushing, just the fill mechanism topping of the tank when the water level falls low enough.

Sorry, I guess I wasn't clear. When you flush the toilet, the flapper doesn't seal the hole and it just keeps trying to fill. Of course, it doesn't happen all of the time. When you lift the lid and watch, wiggle the flush handle enough, it will start to fill. Nothing seems to be interfering with the plastic string between the flush handle and the flapper valve.

There needs to be play in the string/chain from the flapper to the handle so the flapper can seat.

If this is a conventional toilet then more than likely you need to replace the flapper. The Fluidmaster red flapper or the Korky red flappers are cheap and EZ to install and are available all over. The red ones last longer with chlorinated municipal water than the black ones do.

Make sure you clean the surface that the flapper seats on. Don't use anything real abrasive. A VERY light pass with the scrubbie side of a wet kitchen sponge works well.

Thanks lurker. I've tried to clean the flapper but not where it seats. I'll try that but will look for the Korky red flapper too.

You most likely do need a flapper and it always pays to clean the flapper seat when replacing the flapper.

You can find the Fluidmaster red flappers at any Home Depot and the Korkys most likely too.

I want to report back and thank people for their help. I got another flapper at HD and when we cut the plastic chain from the flush knob to the top of the flapper, I noticed that the chain had got hard and turned a bit on itself. So I think that turn was interfering with the flapper valve seating. It was bothering me because everything looked just fine and I couldn't understand why it wasn't working perfectly. Thanks all. Problem Solved!