In a perfect world, we would all own our homes “free & clear.” But this is not possible. Unless you have an allodial title to your property (which is practically nonexistent in the US), you don't really own your home, even if you don't have a mortgage since you have to pay property taxes.
Similarly, you may ask, do you own the airspace over your house?
While the Supreme Court hasn't explicitly accepted that as the upper limit of property ownership, it's a useful guideline in trespass cases. Therefore, unless you own some very tall buildings, your private airspace probably ends somewhere between 80 and 500 feet above the ground.
Can you shoot down a drone over your property?
Law enforcement can deploy these technologies, but under current law it's illegal to shoot down a drone, even if it's hovering above your own property. Increasingly, government is regulating drones and drone flights both at the state level and by the FAA.
Do condos own the land?
In general, each condo unit owner owns a percentage of the land collectively as dictated by the declaration and/or its amendments. The first owners buy the units from the developer. However, the individual condo owners all own a share of all common property (pools, recreation facilities, etc.) which includes the land.