In the words of the Second Doctor, a helicopter was a "primitive form of flying machine". They were also known as choppers and "whirly birds".
The Fourth Doctor found a design of a helicopter in the laboratory of Leonardo da Vinci, in 1505, and commented that the idea "took a bit longer to catch on". (TV: City of Death) Jamie McCrimmon, from the 18th century, could not recognise one in the 21st century. (TV: The Enemy of the World)
They were frequently used on Earth by the military, as they didn't need runways to land or take off.
20th century edit
On 22 December 1963, the Swiss mountain patrol sent a helicopter to evacuate Miss Tremayne's school when Lt Peter Sandoz did not report in; however, Peril Bellamy's telekinesis was activated, turning the wind into a cyclone which crashed the copter and killed the pilot. (AUDIO: Winter for the Adept)
In 1968, Victoria Waterfield was kidnapped by the seaweed-possessed John Robson in one of Euro Sea Gas's helicopters, and the Second Doctor and Jamie McCrimmon were flown out to Rig D in another in order to rescue her. After appropriating Robson's helicopter to enable him and his companions to escape from the rig, the Doctor mentioned once they were in the air that he had learnt how to fly a helicopter by watching Astrid Ferrier, but also pointed out that he wasn't sure how to land it. (TV: Fury from the Deep)
In the 1970s, Brigadier Lethbridge-Stewart had his own personal helicopter, which was used by Captain Mike Yates and Sergeant Benton to fly to Devil's End. It was destroyed when it struck Azal's heat barrier, which was surrounding the village, killing Tom Girton. (TV: The Dæmons)
21th century edit
In 2011, helicopters frequently patrolled the area surrounding Gwen Cooper's house in Wales. This aroused her suspicions as she was in hiding, but Rhys Williams passed it off as army practice. Following "Miracle Day", an armed helicopter was sent to kill her. Gwen destroyed it with a bazooka after a short chase. (TV: The New World)
In 2012, Henry van Statten had a personal helicopter with the call sign Bad Wolf One. (TV: Dalek) The Fortitude sent a helicopter to rescue members of an Antarctic expedition. The Seventh Doctor used it to return to the Ice Warriors. (AUDIO: Frozen Time)
On one occasion, UNIT noticed the Doctor's TARDIS standing in a field. Seeking his assistance with a mystery in the Under-Gallery, they picked it up with a helicopter to transport it back to headquarters. Unbeknownst to them however, the Eleventh Doctor and Clara Oswald were on board at the time. The Doctor crossly called Kate Lethbridge-Stewart from the TARDIS, as the helicopter flew them over London. Kate apologised and had the machine and its occupants brought directly to the "scene of the crime" at the National Gallery. (TV: The Day of the Doctor)