CYA Disclaimer: The following is intended for reference purposes only and not as legal advice.

The short answer is, "as much of it as you can use". No, you cannot float a "No Trespassing" blimp and shoot down passing airliners for trespassing. But believe it or not, you can build a tall building on your property and the airlines can't make you take it down even if it interferes with air traffic - unless you can find a law (such as building codes) that expressly prohibits you from doing so. By federal law, upper airspace is considered "navigable", meaning the public has the right to use it. But what exactly is "upper airspace"? In the foregoing example, if you built a tall building on your land and the airline were overflying your property at altitudes lower than the height of your building (and in the same vicinity), it would be possible for you to sue them for trespassing.

It would also be possible for you to sue for nuisance even if the planes didn't even overfly your airspace, if the planes were making enough noise to interfere with your "quiet enjoyment" of your property. Keep in mind, though, that if you live near an airport, the airport has probably already purchased the right to make as much noise as they want. If you don't know about any such purchase, it's probably because these rights were purchased from a previous owner of your property.

I've got some good news, though, if a new airport is being built near property you own - you might be able to make them pay for the right to pollute your airspace with noise, regardless of whether their planes will be overflying your property or not. If the airport is government-owned, you could claim that the noise constituted a "taking" of your property and although you couldn't stop them from doing it, you could demand "just compensation" (note that the legalese is in quotation marks). If the airport is privately owned, you could file a claim under nuisance law and force them to choose between either continuous liability under nuisance law or settling with you in lump sum for the reduction in the value of your property.