Airplanes, or aeroplanes, are a type of fixed-wing aircraft, driven by a propeller or by jet thrust, which is supported in air by dynamic action.
The first successful "flying machine" was invented at the turn of the 20th century by two Ohio brothers named Orville and Wilbur Wright. They made their first successful flight on December 17, 1903. Eventually, they were able to get almost 30,000 feet in the air. In 2153, Bethany taught a classroom of schoolchildren about the Wrights' airplane while on a Skagaran planet. (ENT: "North Star")
Technological advances in aviation technology made aircraft play a crucial role during the Second World War. These military aircraft were flying well into the 22nd century, where they appeared in air-shows. Jet-engine technology was well developed after this period, and jet aircraft included civilian and commercial airplanes, in addition to fighter jets. (ENT: "Storm Front", Star Trek IV: The Voyage Home)
In 2371, the crew of USS Voyager discovered an ancient Earth aircraft on the surface of a planet which was the source of an automated distress call. It was discovered to be the aircraft belonging to Amelia Earhart and Fred Noonan. In 1937 they among the first Humans to attempt circumnavigating the Earth. During their flight the plane and its two passengers were abducted by the Briori and taken to the Delta Quadrant. (VOY: "The 37's")
During one of the missions in the holosuite program Julian Bashir, Secret Agent, Julian Bashir met up with a beautiful female secret agent who had just jumped out of an airplane at 20,000 feet, yet did not have a hair out of place. (DS9: "A Simple Investigation")