It doesn't matter what is plugged into the GFI circuit, but rather where the outlets are located. Are any of the outlets on that circuit in the kitchen, garage, out on the porch, in an unfinished basement or bathrooms? My guess is that you have one of the items listed above, and someone installed the GFI in a convenient location "upstream" of the outlet that requires the protection.

The situation you describe is often done in ungrounded systems. Also sounds like it is acting as a surge protector.

"Also sounds like it is acting as a surge protector."

Possibly purely by accident.

Thanks for the advice guys, I guess I need to do some more investigation on the circuit. I thought I had traced out all the outlets but maybe I missed something. I'm almost certain that there are no outlets in a wet area or branches off of the main cable on that circuit that could go outside the house. Another question, do GFI breakers ever go bad, or could this one just be defective? I suppose I could find that out myself by replacing it with a new one, this time a 20A. If I don't find anything I missed before that might be the problem and a new GFI doesn't do the trick, a call to a local electrician may be in order.

Yes, they sometimes go bad, as do most electrical components. I had several fail last summer due to nearby lightning strikes.