Closely associated with Doctor Who and his ship, TARDIS, police telephone boxes were once widely used by the cops in the United States and the United Kingdom.
Taking advantage of the new invention of the telephone, which was an advancement to the widely used telegraph system which had been invented and in use for almost 30 years. In 1877, a year after Alexander Graham Bell invented his famous communication device, the first police telephones were installed at stations and the mayor's office in Albany, New York. Other cities like Detroit and Chicago followed suit, soon after.
The world's first known police call boxes was created in 1883 by The Gamewell company and appeared on public streets in Washington, DC. These boxes would easily give the general public and the police, the ability to call stations in case of an emergency. These boxes soon appeared in other cities including Detroit, Chicago, and Boston. The boxes helped police answer to crimes more quickly and cut back on the cost and number of patrolmen used on the streets. The Chicago Police's boxes had a phone which could only be used by the cop and a signal device which could be used by anyone, with 11 different signals (for things murder, robbery, etc.) to notify authorities (via Morse code) in case of an emergency.
The first police call boxes in the UK appeared in Glasgow in 1891. These boxes had gas lanterns on top of them, and were controlled by a signal at the station to go off when police were needed.
By the 1930s, the London-area Metropolitan Police started using the familiar blue kiosk boxes; they were made of wood and later concrete. Each of these boxes had a phone on directly linked to police stations, so cops on the beat could keep in touch with their bosses. The inside of the boxes usually had a stool, a desk or a table, an electric fire device, plus an extinguisher to put out the fire, and brushes and dusters to keep it clean.
By the 1950's and 60s, new technology like walkie-talkies and hand-held radios, made the boxes obsolete and they were slowly phased out. The last original boxes in the UK were put out of use in the 1990s.
Recently, similar boxes have introduced in various cities in the UK, such as Glasgow, London, and Liverpool, which contain, CCTV cameras.
Sources:
http://www.met.police.uk/history/policebox.htm
http://www.eee.strath.ac.uk/r.w.stewart/boxes.pdf
http://en.wikipedia.org/wiki/Police_telephone_box