If a neighborhood kid gets a drone for his birthday and innocently flies it over my house that's one thing but if some perv reptile is snooping around my house with a drone then I'm gonna take the shot and the FAA can come and get me if they want.
It depends on who's doing it. Privately flying a drone over private property is likely a no-no in most situations. However, some other instances will allow for flights over your property--they'll have an easement. In those cases, you could no more shoot down a drone than you could a commercial airliner passing overhead. You control the airspace over your property a whole lot less than you might think. One thing is for sure: this will become a "thing" and we'll need to address it as a society.
Legal clarity would be helpful, but in the meantime this sounds like one of those times when it's good that there's jury nullification as a last resort.
No one can fly a drone or non-piloted aircraft over my home legally because I'm on a flight path approach to an airport (an exception can be made with FAA approval - for example a local firm gets permission to use a drone to inspect roof tiles).
It's different everywhere, but most states recognize property lines above the ground. For example, if a neighbor's tree has a branch extending over your property line, you're usually well within your rights to cut off the part that's over your line. How far up those property rights extend is the question.