Privacy concerns are at their highest when police officers seek to enter into a person's home. This means that except in emergency (called "exigent" in criminal law) circumstances, police officers must obtain search or arrest warrants before entering suspects' dwellings. (To learn more about the plain view doctrine and other exceptions to the search warrant requirement, see Search Warrants: What They Are and When They're Necessary.)
Example: Police officers are in hot pursuit of an armed robbery suspect. If the suspect runs into a dwelling, the police can follow and arrest the suspect.
Example: A police officer walking by an apartment house hears loud screaming coming from one of the apartments. In order to prevent injuries, the officer can use force if necessary to enter the dwelling without having to obtain a warrant first.
In order to gather information to support an application for a search warrant, law enforcement officers are allowed to take aerial photographs or come close enough to overhear conversations. However, they probably cannot use sophisticated equipment to discover what is on your property or to eavesdrop on your conversations (unless, of course, they already have obtained a warrant or qualify for one of the warrant exceptions).