The Washington Post has an article discussing the potential legal implications of drones that stray onto nearby private property. It notes that in the absence of aviation regulations prescribed the use of government airspace, many homeowners are unable to restrain budding drone hobbyists.
The common law standard for ownership of airspace above ones property (so-called ‘air rights’) has been a contentious part of legal history.
Most common law countries have moved far beyond the 13th century edit of “Cuius est solum, eius est usque ad coelum et ad inferos” or “whoever’s is the soil, it is theirs all the way to Heaven and all the way to hell”.
Today the standard has been reduced to a ‘use it or lose it’ standard such as “at least as much of the space above the ground as he can occupy or use in connection with the land” (see United States v. Causby).
In Australia, many pieces of legislation have sought to limit the rights of home owners to sue for trespass or damage resulting from low flying aircraft [see Damage to Aircraft Act 1999 (Cth) for example]. However, currently there is no clear legislation dealing with the issue of hobbyist drones and privacy.