The pigeon was a type of bird indigenous to Earth. Another type of pigeon once native to Earth was the Passenger pigeon.
In 1986, several pigeons congregated in front of Gillian Taylor's stopped Chevrolet truck. (Star Trek IV: The Voyage Home)
The holographic recreation of the Café des Artistes in Paris in the year 2342 featured a small flock of pigeons. (TNG: "We'll Always Have Paris")
In 2365, Miles O'Brien said "Time to pluck a pigeon", commenting upon Data's supposed naiveté of poker. (TNG: "The Measure Of A Man")
In 2374, Vic Fontaine told Odo that in his usual stiff posture he'd only attract pigeons, but not women. (DS9: "His Way")
In that same year, a holographic Leonardo da Vinci remarked to Kathryn Janeway that he only heard the cooing of pigeons and the babbling of fools in Florence, while the King of France admired him. (VOY: "Concerning Flight")