Large Rideable Flying Creatures are called Planes.
They made castles obsolete.
While the term castle is somewhat fuzzy, I will take it to mean a static, fortified location designed to withstand enemy attacks.
Many people believe that the advances in cannon technology such better propellents and rifling killed the castle, but the Trace Italienne pattern evolved to counter such advances in artillery design and technology. The use of very deep earth and brick hills (for they are too wide to be called walls) quite successfully creates a fortification that will resist canon attacks.
The next evolution in castle design came about due to advances in high explosive, making the Trace Italienne's wide thoroughfares very vulnerable to plunging fire from mortar or artillery shells. Cutting a long story short (see wikipedia), forts eventually moved underground, exposing only their guns to the incoming attacks.
What really killed the fortification as a doctrine of war, and made it largely irrelevant were advances on two fronts: Air Power, and increased mobility brought about by advances in Mechanisation. Fortifications would from now on either be destroyed with overwhelming force from the air, or circumvented altogether.
While Mechanisation and mobility can be countered by a determined defender, such as miles of barbed wires, tank traps, machine gun and anti-tank gun positions - or the equivalent in a fantasy setting, nothing at all can be done for air power. Once warfare takes to the air, the era of static fortification is at an end, and the era of air superiority has began.
Even creatures only capable of carrying a payload of 180kg kilograms at most (two fully equipped riders) would make mincemeat out of most modern fortifications with sufficient numbers. Flying high enough to be out of reach of conventional projectile weapons, the attackers are free to bombard the fortification with impunity. This is especially true for a world with either technology or magic, where projectiles can pack an enormous punch for very little weight - think only of greek fire for a real example from antiquity. The only defence against such an attack would be for the fort to keep a force of flying creature itself to be used as counter measure. This would essentially be the race for air superiority.
In fact, the most likely outcome would be that forts give way to a stopping and feeding point for the defender's fleet of air beasts. In effect, airports for flying beasts. This would also have a drastic effect (although dependent on the flight time), on a base's projection of power. The area that one could reasonably control with a flying beast is an order of magnitude larger than with a walking one.
In addition, it is unwise to discount the power of artificial selection. Artificial selection allowed humans to turn the wolf into both the Chihuahua and the Saint Bernard long before we understood genetics meaningfully. Applied to flying creatures, it is easy to envisage a variety of creatures specialised for different roles. here are a few to give an idea:
- Large, slow but sturdy Bred for endurance, they are the preferred breed for long distances or heavy loads. They require little maintenance and have exceptional all round health. Sky camels.
- Small, light and fast This fragile breed is prone to sickness and requires a great deal of care during their rearing. But boy are they fast. Used for scouts and messengers, they can fly twice to three times the speed of most other breeds. Air Arabian Horse.
- Tough and mean When you need to take down other flying creatures, these are the ones you go for. You don't burden them with a rider (They won't really support one anyway) and you lead them from another creature. Their viciousness is legendary and most tamers are missing a limb or two, but a squadron of those over your lands will deny the skies to anyone else. (You might also lose a sheep once in a while). Sky Wolves.
- Marine This breed deals with the difficulties of sea travel better than any others. In fact, they will mostly feed themselves on long sea journeys by dive fishing. Special boats accomodating dozens of the breed can project power over the ocean and assail distant cities. Portuguese Water Dogs for the clouds.
- Smart & cooperative Bred for a pack mentality and a superior intellect this breed excels at complex tasks requiring timed coordination and planning. They take orders via hand signals and are the preferred breed for covert or special force work. If a silent night-time assault is required, your elite soldiers will most likely be riding these guys. German Shephards.
An interesting idea would be for some breeds to be the secret pejorative of a given nation. This would lead to the nation only fielding a single gender of the breed to avoid other nations capturing or breeding similar beasts, downded riders killing their beasts the way modern special forces destroy downed helicopters with explosives, or perhaps only fielding castrated creatures.
The wider issues
You'll also need to think of the wide spread effects of having air travel from pre-history. Political and Social systems would look very different indeed if humans had air travel before writing. In fact, flying creatures would be a world-defining feature. The entire history of exploration and map-making, as well as the differences in advancement and technology on earth would likely never occur.
Rapid exploration and communication would have drastic and fundamental effects. Languages would evolve differently, and trade routes would also be very different, as they would no longer have to be defined by geography. This is only scratching the surface.