Flying Bike

If your tech base has anti-gravity worked out, you may have a Flying Car that's actually practical - it bypasses most of the issues surrounding driving over unyielding terrain simply by flying over it, and manages to maintain some decent fuel economy while driving faster than a conventional sports car. But then, being practical is not the only desirable quality, and since on the ground motorcycles have been seen as the absolute coolest way to travel, why not a Flying Bike, too? Especially if the cast features an Badass Biker who has his signature hover bike.

As with cars, Flying Bikes range all the way from the Not Quite Flight of hover vehicles to space-capable flight (which may require extra Handwavium for radiation shielding). And it comes with the added risk of falling off your bike (painful when the bike's on the ground, potentially fatal at 500 feet)... and potentially into something that you can't normally stand on, like a lake of magma.

Anime and Manga

 * REDLINE has a hoverbike that JP uses to get around Europass.
 * Woody's flying delivery bike in Aria is fast enough to turn what would be a month-long voyage by gondola into a day trip by air.
 * The bandit troop that Dagmyer recruits to his uncle's cause in Tenchi Muyo! War on Geminar are liberally equipped with vehicles that look suspiciously like the speeder bikes from Star Wars. Eventually the good guys hijack a couple.

Comic Books

 * Lobo has his Space Hawg. Which sometimes has wheels installed, but generally used as personal spacecraft.

Fan Works
""Holy shit! He just popped a wheelie and kept going up!""
 * Doug Sangnoir, the Original Character protagonist of the Mega Crossover series Drunkard's Walk, owns a flying motorcycle that he built early in his travels through the universes. It's mentioned that he has another one at home.

- from a post by Bob Schroeck on the Drunkard's Walk Forums

Film

 * Star Wars has a wide variety of repulsorcraft, including speeder bikes. Stormtroopers use these for scouts (then an Ewok stole one of those, and was surprisingly familiar with piloting it).
 * The expanded canon shows that speeder bikes have been around since the Clone Wars, although they were generally used by pirates as a means of reconnaissance and raiding.
 * Flash Gordon had a Hawkmen rocketcycle piloted by the protagonist at one point.
 * Playing With a Trope: The most iconic scene in E.T. the Extra-Terrestrial has Elliot on a bike with ET, Elliot's friends on their bikes behind them, all flying.

Literature

 * Vorkosigan Saga has "float bikes".
 * In Phule's Company, Chocolate Harry gets official permission to use his personal hoverbike instead of a Legion vehicle. He had experience with hoverbikes, having joined the Legion after a bad squabble with a biker gang.
 * Sirius' flying motorbike from Harry Potter.

Live-Action TV

 * In Galactica 1980, the Colonials bring flying motor bikes to Earth.
 * Power Rangers has at least three flying bikes, each for a single Ranger in its season. Such as custom made "Hovercraft Cycle", a wheeled bike with flight mode.

Music

 * Judas Priest's Painkiller is a chrome-plated cyborg angel riding a flying dragon-motorcycle with buzzsaws for wheels, according to the song and the album cover.

Tabletop Games

 * Warhammer 40,000 has jetbikes, used mostly by the Eldar. Space Marines used to ride them too, but in later supplements they're Lost Technology, so only a few remain in working condition (although the White Scars use them en masse and the Dark Angels have a company's worth of them). Necrons have Tomb Blades, which are somewhere between tricycles and monowheels in shape.
 * Star Frontiers have hovercycles. Like other hovercraft, they are somewhat less manoeuvrable than other vehicles, but unlike other hovercraft they have lower top speeds than the wheeled version. Having sapient flying squirrel/monkey hover-bikers in sunglasses is its own reward.
 * Stars Without Number also have hovercycles. A PC (as a VI Vehicle Bot) might be one. Hover vehicles are not-quite-flight, but can briefly raise to 10 m, thus can usually move through anything short of dense vegetation or Kowloon Walled City grade urban terrain.

Video Games

 * The Star Wars: Battlefront games generally have Speeder Bikes as a means for going from "Point A" to harassing an enemy command post in a matter of seconds. But, being a vehicle that leaves the operator exposed, it's essentially an Fragile Speedster that can be commandeered by killing the person riding it.
 * Mario Kart 8 introduces the concept of anti-gravity, with the vehicles' tires being reconfigured so that they can float above the ground (and walls). And it's worth mentioning that motorcycles makes a return in this instalment.
 * Wes from Pokémon Colosseum has a hoverbike monstrosity. It even has a side car that his Espeon and Umbreon ride in.
 * The Hoverbikes in X-COM: Apocalypse; since they can be armed and are very agile, Zerg Rushing massive Flying Saucers with Hoverbike swarm works fairly well. The downside is that since a bike can take only a small weapon and a basic targeting system, crippling or killing large targets takes many shots, so the battle tend to protract — and cause more damage to the city, since that's what missing shots from whoever is at the greater altitude usually do.
 * Perfect Dark has a hoverbike, from Area 51.
 * The opening scene of Mega Man X 2 has X riding a hoverbike.
 * Flashback has the protagonist running on one of these in the intro cutscene.

Web Comics

 * In Book 15 of Schlock Mercenary, Sorlie's bosses send a scooter to pick her up while jumping from the flying car she was riding in. Later the entire team gets scooters and flying cars. Remote control allows them to Land in the Saddle smoothly, or use scooters as kinetic missiles.
 * Sluggy Freelance has inflatable hoverbikes. Riff got them from a Mad Scientist inclined to make everything inflatable.

Western Animation

 * Code Lyoko has an "Overbike".
 * By the third season of ReBoot, both Matrix and AndrAIa ride flying bikes instead of using their home system's usual hoverdisks to get around.