Dragons are found in the myths of many cultures, and appear in many different configurations. The name comes from the Greek "draconta" which means "to watch." Often, dragons are portrayed as guarding an object or a particular area.

Types
In Western myths, dragons are generally dangerous carnivorous reptiles, and can be categorized by their appearance or habitat. Categories by appearance covered the various combinations of legs and wings-
Guivre (no legs or wings, just a large serpent with a dragon head.)
Lindworm (one pair of legs and no wings.)
Wyvern (one pair of legs, and wings.)
Amphiptere (No legs, but wings.)
Heraldic Dragon (two pairs of legs and wings.) as seen above.
Habitats included:
Caves
Mountains
Rivers, Lakes, and Ocean
Swamps

Chinese Dragons are also reptilian, often combined with parts of other animals. They symbolize power and are generally considered good fortune. These dragons can be grouped by function:
Celestial- Guardians of the houses of the gods-these dragons were the only ones with 5 claws.
Divine- controlled the wind and rain.
Terrestrial- River dragons- controlled the flow and course of rivers.
Subterranean- Keepers of treasure-generally seen holding a pearl.
The Chinese had other systems to determine the dragons strength- color and age. Red or black dragons were ferocious, but not as powerful as yellow ones. Some believed that dragons came thousand-year-old snake eggs (dinosaur eggs?) or that water snakes became dragons after 500 years. After a thousand years, the dragon would grow four feet and a beard. After another 500 years, the dragon would grow horns, and after three thousand years the fully-mature dragon would get its wings. Dragons can be seen in the shapes of clouds.
Japanese and Korean Dragons are much like the Chinese. Chinese ones will normally have 4 or 5 toes, while Japanese ones normally have 3 toes.
Many other cultures have legends of dragons. For example, the Sumerians spoke of Tiamat, which was a huge female dragon with two legs and horns. Native American Seneca myth tells of Gaasyendietha, a dragon that lives in the water but can shoot fire.