Several designs exist (such as Moller's skycar), but while several (such as the Convair flying car and Molt Taylor's Aircar) have flown, none have enjoyed commercial success.
In the 1950s, Ford Motor Company performed a serious feasibility study for a flying car product. They concluded that such a product was technically feasible, economically manufacturable, and had significant realistic markets. The markets explored included ambulance services, police and emergency services, military uses, and initially, luxury transportation. Some of these markets are now served by light helicopters, proving the accuracy of Ford's marketing. However, the flying car explored by Ford would be at least fifty-fold less expensive.
When Ford approached the U.S. Federal Aviation Administration about regulatory issues, the critical problem was that the (then) known forms of air traffic control were inadequate for the volume of traffic Ford proposed. At the time, air traffic control consisted of flight numbers, altitudes and headings written on little slips of paper and placed in a case. Quite possibly computerized traffic control, or some form of directional allocation by altitude could resolve the problems.
As the successive decades since failed to deliver such a vehicle, the flying car became somewhat of a totem of the failure of futurism to accurately predict the future development of society and was regularly used to poke fun at futurists.
The novels of Philip K. Dick and the film Blade Runner, in particular, feature VTOL flying cars, in the form of "flapples" and "skimmers" respectively. More recently, flying cars have made the transition from science fiction to fantasy in the Harry Potter books, in the form of an otherwise-stock (and long since obsolete) Ford Anglia enchanted to fly.
See also Transport, Automobile, future of the carFictional