Other

Various fantasy creature have crept into furry fandom as accepted types of furs, mainly griffins, dragons, hippogryphs, and other such large fantastic animals.

Callander, Don "Dragon Companion " (fantasy-dragon)- out of print

A dragon appears to a quiet employee of the Library of Congress and whisks him away to a magical kingdom where librarians are among the most powerful of humans, especially if they are a dragon's best friend.

Callander, Don "Dragon Rescue " (fantasy-dragon)- our print

More than ten years after the disappearance of young dragon Arbitrance Constable, his best friend, Murdan of Overhall, suspects that Arbitrance is not really treasure hunting and rallies the Constable family into beginning a search.

Lackey, Mercedes and Larry Dixon "The Black Gryphon" (gryphon, reptiles-fantasy)

from the back cover:
Skandranon Rashkae is everything a gryphon should be…
with gleaming ebony feathers, majestic wingspan, keen magesight, and sharp intelligence, he is the fulfillment of all the Mage of Silence, the human sorcerer Urtho, intended to achieve when he created these magical beings to be his champions, the defenders of his realm- a verdant plain long coveted by the evil mage Ma'ar.
And now, as Ma'ar is once again preparing to advance on Urtho's Keep, this time with a huge force spreaheaded by magical constructs of his own, Skandranon is sent to spy across enemy lines, cloaked in the protection of Urtho's powerful Spell of Silence.
As days pass and Skandranon doesn't return, all in Urtho's camp wait anxiously. But there is one among them for whom the possible loss of this great bird will be more than just a major military defeat. Amberdrake- a Healer of body, mind and spirit whose talents are as essential to the army as those of any general- waits on the landing strip with anguish in his heart. For Amberdrake has come to value the vain, cocksure and brave Skandranon as his closest friend and comrade, and he now fears that this prince of gryphons will never return…

McCaffrey, Anne "Dragonflight" (dragons-fantasy)

Book I of the Dragon Riders of Pern series. (though you can read them out or order)

From the back cover:
Lessa's last chance
After ten long Turns, Lessa was ready to come out of hiding, to reclaim her birthright… and to Impress the young dragon wueen and become Weyrwoman of Benden.
Suddenly the deadly silver Threads once again theatoned all Pern with destruction. But the mighty telepathic dragons that for centuries had defended Pern were now few in number, not nearly enough to protect the planet in its hour of greatest peril. Then Lessa hatched a daring and dangerous scheme to rally support from people who had long ago ceased to exist!

McCaffrey, Anne "Dragonquest" (dragons-fantasy)

Book II of the Dragon Riders of Pern series. (though you can read them out or order, there's a summary of the plot so far at the beginning of the book)

From the back cover:
Dragonfire
Another Turn, and the deadly silver Threads began falling again. So the bold dragonriders took to the air once more and their magnificent dragons swirled and swooped, belching flames that destroyed the shimmering strands before they reached the ground.
But F'lar knew he had to find a better way to protect his beloved Pern, and he had to find it before the rebellious Oldtimers could breed any more dissent… before his brother F'nor would be foolhardy enough to launch another suicide mission… and before those dratted fire-lizards could stir up any more trouble!

McCaffrey, Anne "The White Dragon" (dragons-fantasy)

Book III of the Dragon Riders of Pern series. (though you can read them out or order, there's a summary of the plot so far at the beginning of the book)

From the back cover:
Never had there been as close a bonding as the one that existed between the young Lord Jaxom abd his extraordinary white drgaon, Ruth. Pure white and incredably agile, Ruth possessed remarkable qualities. Not only could he communicate with the irridescent, fluttering fire lizards, but he could fly back in time to any WHEN with unfailing accuracy.
Nearly everyone else on Pern though Ruth was a runt who would never amount to anything, but Jaxom knew his dragon was special. In secret they trained to fight against the burning threads from the Red Planet, to fly back in time as well as Between, and finally their close and special union was to result in the most startling and breathtaking discovery of all…