The main definition of a dragon is 'a fabulous animal usually represented as a monstrous winged and scaly serpent or saurian with a crested head and enormous claws'. Dragons come in many shapes, the most common known are the Western Dragon (thick, long bodied, scaly skin, four strong legs, two bat-like wings, wedge-shaped heads, and long necks) and the Eastern Dragon (serpentine bodies, have four legs, they do not usually breath fire, do not have wings, but there are rare cases that do).
Others are the Faerie Dragon, which have practically no history due to its rare sightings. The Hydra, often seen in Greek mythology. The Drake, which is a basically a Western Dragon mixed with an Eastern Dragon. The Ouroboros, the famous dragon that bites his own tail making his body a circle, representing the Universe, eternity or never-ending. These pictures are just a handful of all the avaible dragons.