It is a little more complicated than what I said.. The article has a pretty good explanation.
In the article: the first case the supreme court heard on the matter was a chicken farmer who said planes flying overhead were scaring his chickens, and they would fly into walls from fright. He had about 150 dead chickens. The planes were flying at 83 ft. He lost that case.
Here's the Wikipedia "air rights" article... it has a section on the US:
http://en.wikipedia.org/wiki/Air_rights
A quote:
Specifically, the Federal Aviation Act provides that: "The United States Government has exclusive sovereignty of airspace of the United States."[2] The act defines navigable airspace as "airspace above the minimum altitudes of flight…including airspace needed to ensure the safety in the takeoff and landing of aircraft."[3]
It also mentions a 500ft min limit for sparsely populated areas. But note, that's a limit set by the FAA. They may lower it or raise it if they want to.
In the wikipedia article you'll also find a quote from a case by a property owner suing a nearby airport. I think it perfectly sums up the rights of property owners with regards to the air.. but it's a little long to post here.