If I am having to put coolant in my radiator every so often, there is no overflow, and I don't have any leaks, would that mean that my head gasket is leaking?

 

check the water pump

 

What's that supposed to mean? You think the water pump isn't pumping, or it's leaking? Could it be leaking into the engine? There are no drips whatsoever.

 

there could be a tiny leak somewhere, check the rad cap, the overflow tank hose and the bottom of the radiator. If you know for sure there is no leak then its possible you have a bad head gasket.. Any other signs of a bad head gasket... Have you had it completely filled while the car was on.. like squeezing the hoses to get the air out and be able to fill the coolant all the way up?
mike