An unidentified flying object, or UFO, was a colloqualism of the 20th and 21st centuries, referring to any airborne object whose nature could not be adequately explained. These craft, also sometimes known as flying saucers, were often speculated to be of extraterrestrial origin, were usually dismissed by official sources as common phenomena such as sun dogs or weather balloons, at least publically.
A model of a flying saucer was kept on a desk in the office of Incredible Tales magazine in 1957. That same year, a news vendor expressed his disinterest in science fiction, listing flying saucers as one element. (DS9: "Far Beyond the Stars")
In 1969, the USS Enterprise NCC-1701, after having been inadvertantly transported back through time from the year 2267, was detected as a UFO by an Air Force base in Omaha, Nebraska. Captain John Christopher, an Air Force pilot, attempted to intercept the Enterprise in an F-104 Starfighter plane, but found he was unable to catch up with it. (TOS: "Tomorrow is Yesterday")
In 2372, the Ferengi shuttle, Quark's Treasure, inadvertently traveled back in time to the year 1947, where it crash landed on Earth in the state of New Mexico. The shuttle was initially found by a farmer before the US Army took possession of the ship and its occupants – Quark, Rom and Nog – who were brought to an nearby base where they were questioned and examined. By bluffing their way out, and with a little help from Professor Jeff Carlson and Nurse Faith Garland, they were able to escape. The incident was later denied, and the wreckage found was decidedly determined to be a weather balloon. The incident was later referred to as the Roswell Incident. (DS9: "Little Green Men")
In 2373, the USS Voyager was transported back to Earth of the year 1996 after encountering the timeship Aeon. Several systems were damaged in the trip to the past, including transporters. Voyager was required to make a close pass over the city of Los Angeles in an attempt to recover the Aeon, which had been stolen by computer tycoon Henry Starling. Natives of the time period recorded Voyager's appearance, and the ship was popularized as a UFO on several news programs. (VOY: "Future's End") The reports were later dismissed as hoaxes and delusions. (VOY: "Future's End, Part II")