Dragons are common in both Eastern and Western mythology. Originally pictured in medieval texts as dog-sized reptilian beasts, with a varying number of limbs, today we think of Dragons as being much larger in general (growing larger than a bus) and having six limbs - two powerful hind legs with grasping talons, two forelegs that may also function as hands, and two wings that are large and strong enough to sustain flight (whether this is also helped by magic is a matter of much conjecture).
Griffins are generally pictured as a hybrid of eagle and lion. Generally these have the hindquarters of a lion and the head and wings of an eagle; front legs may vary in different subspecies between lion or eagle like. Other, generally smaller, species may be formed in the guise of other birds and other felines - such as crow/domestic black cat or osprey/cheetah. Griffins are often found in heraldry, as the lion and the eagle were both considered the kings of their realms. They are also often thought to place gold around their nest, as their beaks are strong enough to quarry it from the ground.
The Jackalope is a Northern American creature, described as a jackrabbit with the horns of a stag. Popular with the taxidermy trade, they are often said to be hunted out of an area, but often pop back up in local stories over and over. Researchers suggest that at least some of the tales of horned hares were inspired by sightings of rabbits infected with the Shope papilloma virus. It causes horn- and antler-like tumors to grow in various places on a rabbit's head and body. Jackalopes are said to be extremely dangerous to hunt due to their sharp antlers.
Kelpies, or water-horses, are most common in Scotland. They tend to live in dark, deep places in rivers or streams, occasionally lakes. There are stories that Kelpies have been known to pull unwary children and travellers into the water. Some Kelpies are shape-shifters, with forms ranging from human, horse (often black), and a part-horse, part-fish or serpent form. The most infamous Kelpie is that which resides in Loch Ness.
In Japanese lore, Kitsune are magical yōkai (shapeshifters) which change between human and fox forms. In some stories, the kitsune has difficulty hiding its tail in human form, and this can be one way of identifying a shifted kitsune. As a fox, the number of tails may indicate their age and power, with nine being the ultimate number - reached, some say, only after a hundred years. Kitsune are often pictured as being wise tricksters, that can grant great boons if amused or if helped. They will often ask for favours in return for aid.
In medieval Greek mythology, there is only one Pegasus (born from the blood of the Gorgon Medusa); but some would agree the species has many individuals, even herds, of the winged horses. Most Pegasus are thought to be white, in order to blend in with the clouds as a camouflage, but some can change colours or are different colours.
The Peryton is a blending of a stag or deer and a bird. Generally the stag predominates, and the bird features may be limited to wings and plumage or coloration. They are most often green or blue. Some tales say the Peryton casts the shadow of a man until it kills one, then it may cast its own shadow. They are thought to be wild and arrogant, and some may have strong magic.
The Phoenix is a bright, beautiful bird that begins and ends its life in flame - it is born from an egg heated by flames, and burns to ash when it dies, leaving behind one egg. This is said to happen very rarely, once in a hundred, five hundred, or a thousand years. Most say there is only ever one Phoenix, being reborn endlessly. It is a symbol of regeneration, fire, and the sun.
Unicorns are described in the most ancient texts as goat-like, but in modern times are most often horse-like. Sometimes the flowing beard and split hooves of a goat persist when depicted with an otherwise horse-like body. The most important feature of a unicorn is the large, pointed, single horn growing from its forehead. This is often described as spiraling, white or iridescent. Unicorns are often thought to be drawn to virgins, especially female maidens. The horn has the power to heal and to remove poisons from water. The unicorn was believed to be the natural enemy of the lion.