In addition to the plethora of Batplanes and other flying vehicles Batman has used over the years, on occasion he has made use of Batcopters.
In addition to smaller Batcopters, Batman has also used the so-called Flying Batcave, a massive helicopter that is equipped with a crime lab and even its own trophy room boasting copies of such objects as the giant Joker card and the Giant Penny. It is also equipped with a massive metal hand for grabbing criminals and a magnet for taking away firearms. However, the Flying Batcave requires frequent refueling, limitings its use.
The Flying Batcave was used only twice, most notably to foil the Condor Gan of Central City.
On occasion, Batman and Robin have been shown to make use of smaller, one seated open air helicopters called the Whirly Bat. For more information, consult the page.
In the Dark Knight Universe of Earth-31 has been shown to have a variation of the Flying Batcave design in his Batcave, seen in All-Star Batman and Robin the Boy Wonder.
In Other Media
In the 1966 Adam West Batman film, the Batcopter makes its appearance. The Batcopter used was a Bell 47 leased from the National Helicopter Service for $750 a day for five days. In film, the helicopter is used primarily for a memetic scene wherein Batman, on a rope ladder of the helicopter, is attacked by an exploding shark that latches onto his leg. He only escapes when Robin is able to give him Bat Anti-Shark Repellent.
The Shark clues Batman into the identity of the members of the Underworld United, as where there are fish, there is a penguin, it happened at sea, and Catwoman starts with a c, the shark attacked by pulling on Batman's leg. All in all, everything added up to a sinister riddle.