A flock of geese, seen on the Amusement Park planet
A goose is a type of bird native to the planet Earth.
A flock of geese flew across the sky of the Shore Leave Planet when Captain Kirk visited the planet in 2267. (TOS: "Shore Leave")
While the USS Enterprise attempted to escape the USS Reliant by entering the Mutara Nebula, Saavik noted that static discharge and gas clouds of the nebula would disable the ships' visuals and shields. Spock noted how her observations were actually to their benefit by replying, "what's sauce for the goose, Mr. Saavik. The odds will be even." (Star Trek II: The Wrath of Khan)
Data once stated he was possibly "pursuing an untamed ornithoid without cause", meaning on a wild goose chase. Spock was also once accused of taking the USS Enterprise on a wild goose chase, to which he replied that he was following logic and not a wild aquatic fowl. (TNG: "Data's Day"; TOS: "The Gamesters of Triskelion")
In 1996, after Rain Robinson discovered a UFO in Earth's orbit, Henry Starling attempted to downplay the discovery by noting that it was probably a flock of geese. Robinson disagreed, as flocks of geese don't park themselves 20,000 kilometers in orbit above Earth. (VOY: "Future's End")