Flying Bike

If you got Anti Gravity worked out, you may have a Flying Car that's actually practical. But then, 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?

As with cars, ranges all the way from Not Quite Flight of hover vehicles to space-capable (may require extra Handwavium for radiation shielding).

Anime and Manga

 * REDLINE has a hoverbike 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.

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 got a lot of various repulsorcraft, including speeder bikes. Stormtroopers use these for scouts (then an Ewok stole one of those, and was surprisingly familiar with piloting it).
 * Flash Gordon had Hawkmen rocketcycle piloted by the protagonist at one point.

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 got experience, and ran to Legion after a bad squabble with some biker gang in the first place.
 * Sirius' flying motorbike from Harry Potter.

Live-Action TV

 * In Galactica 1980, the Colonials bring flying motor bikes to Earth.

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 cover.

Tabletop Games

 * Warhammer 40,000 got jetbikes. Mostly the Eldar. Space Marines used to ride them too, but lately it's a bit of Lost Technology, so only a few remained in working condition. Necrons have Tomb Blade, which is somewhere between tricycle and monowheel in shape.
 * Star Frontiers got Hovercycle — as all hovercraft somewhat less manoeuvrable, but unlike other hovercraft they have lower top speed than the wheeled version. Maybe having sapient flying squirrel/monkey hover-bikers in sunglasses is its own reward.
 * Stars Without Number got Hovercycles. A PC (as VI Vehicle Bot) may be one. Hover vehicles are not-quite-flight, but it can briefly raise to 10 m, thus usually can move through anything short of dense vegetation or Kowloon Walled City grade urban terrain.

Video Games

 * 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 got a hoverbike, from Area 51.
 * 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

 * Schlock Mercenary Book 15 escalates action when Sorlie is given by her bosses [//www.schlockmercenary.com/2014-11-10 a scooter], delivered to pick her up while jumping from the flying car she currently rides. Later the entire team gets scooters and more flying cars, both as transport and as kinetic missiles.
 * Sluggy Freelance got hoverbikes. Inflatable ones, thanks to the Mad Scientist inclined to make everything inflatable.

Western Animation

 * Code Lyoko got a hoverbike. Er, "Overbike".