Vekoma, a company usually known for their cheap selection of rides and/or cheaper knockoffs of the current trends (such as the SLC with the inverted coaster trend), took the helm of innovation with their Flying Dutchman coaster, the first coaster to give riders a true sense of flight by lying them down on their backs and flipping them into the prone position at certain points in the ride. Since then, two companies have produced flying coasters - B&M, who's "true" flyer is considered the best version availible today, and Zamperla, who's cheap and somewhat painful version is to Flying coasters what the SLC is to inverted coasters.
The Original
Vekoma Flying Dutchman
The first flying coaster was made by Vekoma, and while technically a flying coaster, is considered more of a lay-down coaster with flying segments. Riders are loaded into the cars facing backwards, and before dispatch, the trains are tilted backwards (see picture) into the lay-down position. At the top of the lift hill, the trains performed a lie-fly element built into a 180-degree turn, flipping them into the flying position. Three such rides exist today, the latter two (X-Flight at Geauga Lake, and Batwing at Six Flags America) replacing the final two corkscrews with inline-twists.
Variations
B&M Flying Coaster
Considered the first "true" flying coaster (due to the loading process in which the trains leave the station in the flying position, unlike the lay-down position of the Vekoma Flying Dutchman series), the first B&M Flying Coaster was the result of a collaberation between John Wardley and B&M, who had worked together desiging the flying coaster since Nemesis was completed in 1993. When the ride was finally under construction at Alton Towers, B&M sold a different version (soon to become the standard version with further other copies being built in the years to follow) to Six Flags, which quickly went up at Six Flags Over Georgia - the American park nearly took the title of first Flying Coaster from Alton Towers, the park who had helped develop it!
Zamperla Volare
A much less technically impressive flying coaster was made by Zamperla, as a compact fairground coaster. Their few installations have combined flying coasters with wild-mouse style layouts, offering constant turns and small dips with single-car trains. The Zamperla version offers the potential for a small park, without money for a Vekoma or B&M flyer, to purchase a coaster of this style.