Police officers are often referred to as cops, but the origins of this nickname are something of a debate. It is known that, up until the 1970s, "cop" was something of a slang term, and one would refer to law enforcement officials more properly as policemen. Some argue that the term is shortened from "copper" and derives from the tin or copper badges worn by a policeman. Others say that it is an abbreviation for "Constabulary of Police."
General consensus on the word origins of "cop," however, suggest that the term is based more on the policeman's job than on his clothing or job title. In Latin, the verb capere can be defined as "to capture." In French, the verb is caper. "To cop" in English is to seize or to take, and this defines some of what a police officer does: he or she seizes or takes crooks or stops their crime "capers."
Some also believe that the Dutch word kapen, which also loosely translates to "to steal or take," is related to policemen being called coppers or cops. Essentially, the police force was there to take criminals off the streets. Since the Latin, Dutch, and French terms are all similar, and since American English especially derives language from German, French, and Latin, the specific language origin of kapen or capere creates a ready path to the slang term.
While it is appropriate to call members of the police force cops, and it is no longer considered derogatory, certain other terms for police officers are definitely insulting and unwelcome. While British Police might not mind being called bobbies, no police members like to be referred to as pigs or the "fuzz." Some don’t mind the term the "heat" as applied to the whole police force, but the police force does not generally take kindly to terms given to them by criminals.
The term is in such common usage now, however, that a show documenting their work on the job is called Cops. Even though J. Edgar Hoover once highly objected to the term, it is now fine to refer to a policeman or a police woman as a cop. The term "police officer" is generally most correct, since it is not gender based, and is slightly less familiar.