During the Pre-Crisis, the Batplane went through more redesigns than any other vehicle. Most of the Batplanes were designed after real military aircraft. As the designs improved the artists and the writers changed the Batplane.
Batman's first vehicle appeared after four issues and it is called the Bat-Gyro. When Bruce's girl friend Julie Madison was hypnotized by The Monk into going to Hungary, Batman follows her in the Bat-Gyro. Batman rescues her and shoots The Monk with silver bullets. The Bat-Gyro was used several times but Batman would later discard it for more advanced versions.
Wave of Bat-Planes
After he was partnered with Robin, the Batplane became more prominent in the comics along with the Batmobile. The first one was a small monoplane with retractable wings but the artists dropped the propeller in place of a bat-shaped head. Later Batman would go on to add jet engines to the Plane.
During this age, all the Golden Age story was said to have taken place on Earth 2. While the new Silver Age stories took place on Earth-1. During this age, Batman's costume had a yellow oval over the bat logo and his cape would be larger and cover his shoulder area. During this time, the Batplane appeared very rarely because the editor, Julius Schwartz, felt that the stories should deal with crime and mystery rather than silly alien threats. However the Batplane managed to appear a few times and gave us 4 new Batplanes. The first one was Batplane 3 (The Golden Age Batplanes being the first two), an F-104 Star fighter with additions like the New Look Bat logo and scalloped wings and tail.
Unfortunately, the Batplane didn't make another appearance till the 1970's This Batplane had four engines and could cruise at 1,243 miles per hour. After that the Batplanes made very brief and unmemorable appearances. The other and the last one to appear before the Crisis on Infinite Earths was Bat Plane 6 which appears as a shrunk F-101 Voodoo and was used several times, to give it the title Bat Plane 6.
Other Flying Vehicles
The Flying Bat Cave
Batman once visited Central City to investigate a crime wave. He brought along with him the Flying Bat-cave, which used smoke generators to create artificial cloud cover to hide it. The Flying Bat Cave was a massive helicopter that contained small crime lab and other amenities of the Batcave. However, it required frequent refueling due to its size, limiting its usefulness.
During the early Silver Age, when Batman stories dealt more with fantastic elements, he visited the future where he used a Bat-rocket to fly around and stop crime in space and on earth. Batman could be alerted with the Bat signal lit from the earth on the moon. The bat-rocket also made a brief cameo appearance in the story arc Batman & Son in Batman #658 issue were it was used to quickly travel from Wayne Manor to a submarine of the coast of Gibraltar.
The Batcopter is Batman's personal helicopter. Although used a great deal in the Silver Age, he now mostly uses the Batwing.
During the Golden Age, Batman employed several of these one seat personal helicopters . They could hold only one person and the Golden Age Batman and Robin used it to chase the original Mr. Freeze to his lair. The Whirly Bat has appeared a handful of times in modern comics as well, such as Batman #673.
During Batman's early years he had to deal with a group of thieves and was unable to catch them the first time. In order to catch them more effectively, Batman designed a Bat-glider and, as in the movie Batman Returns, Batman kept the rigid glider folded into a harness behind his cape. As Batman chased the thieves into a graveyard, one of them threw a hook at him, which went through the glider, tearing it, so that Batman fell from the sky and into a tree. Later, Batman would encounter Man-Bat whose predatory nature catches the thieves. Later Batman and Man-Bat would fight in the Batcave. Batman was able to defeat the stronger and agile Man-bat without the glider. However, Batman still keeps a glider for himself although he uses it very rarely.
The Current Batwing
Although the Batwing has been absent from the comics for some time, Batman occasionally uses one of the JLA's vehicles during their missions. In a modern retelling of Batman's history in Batman Confidential, the Batwing is from the Wayne Tech and Bruce Wayne borrowed it from them to use it against Lex Luthor. A modified Batwing had appeared in Detective Comics #750 in November 2000. Its basic design is taken clearly from the 1989 movie Batman and from Batman: The Animated Series. Batwing can call the Batwing by pressing a button on his gauntlet, he can turn it on and make it available.
Batwing: Batman uses a Batwing obviously based on Tim Burton's 1980's Batman movie. The design was altered a bit so that the wings appeared more streamlined.
Bat-glider: Batman also used a Bat-glider in this series, though they look more like normal gliders with black handles and are bat-shaped. Handy when it comes to battling foes like Man-Bat. Batman also uses them for stakeouts and surveillance.
The New Adventures of Batman
Batglider: was upgraded as well and now had a more rigid metallic design. This version is apparently jet powered and can now fire missiles. When Gotham's new mayor, Maximillian Zeus, adopts questionable tactics in defending Gotham, Batman has to infiltrate his airship 'New Olympus' with a high tech Batwing. This new version is lightweight, fast and more reliable. It can [has? / can have?] a pod for a cockpit and Batman wears a special suit while in it. There are also pods located on the wings, possibly for other passengers. When Batman tracked down the Penguin's birds when he was on a crime spree. Batman mostly uses the glider against flying opponents like Man-bat, Firefly and Roxy Rocket. As with the modern age, this Batglider is jet powered and it is once again folded into a harness behind the cape.
Lego Batman: a Batglider appears but is called Batwing.
Arkham Games: a Batplane-like vehicle is seen hanging from the ceiling and covered by a tarp inside a Batcave under Arkham Island. Later Batman remotely pilots the Batplane to his location and has it drop off one of his gadgets, the Line Launcher. At the end Batman calls it again to leave for Gotham. This vehicle appears again in Arkham City.
In The Dark Knight Rises trailer a flying vehicle similar in appearance to the Batmobile is seen.
In Batman Arkham Origins, you could take fast travel from one part of Gotham to the other. Batman frequently used the Batplane in this game to travel from Gotham to the Batcave and from the Batcave to Gotham.
The Batplane also appeared in the movie Son of Batman, where Batman uses it to travel, and Nightwing uses it to help Batman with the Man-Bats.
Batman uses the Batplane in Justice League Throne of Atlantis. The Batplane isn't shown that much, but the first time it gets shown in this movie, was when Batman was hunting down Scarecrow thugs. The second time was when Batman helped Aquaman take out forces of Trenches with artillery from the Batplane.