Except for a brief introduction, I am going to limit my discussion of these dragons to their physical characteristics to avoid spoilers. If you want to know more about the dragons, click on the links to visit their full descriptions on 'A Wiki of Ice and Fire', my source for this article.
At the start of George R. R. Martin's fantasy series, A Song of Ice and Fire, and the popular television series based on it, dragons were considered extinct. However, they had existed in the past, and were a part of the history of the world. That changed when Daenerys Targaryen hatched three eggs and became the Mother of Dragons.
Daenerys named her three dragons Drogon, Rhaegal and Viserion. Drogon was believed to be a reincarnation of another dragon, Balerion. He was black with red horns and spines. His eyes were red, and his blood was black. Rhaegal had green and bronze scales. His eyes were bronze and his teeth and claws were black. Viserion was cream colored, with gold on his horns, wing bones and spinal crest. His eyes were gold and his teeth were black. He was called the white dragon.
Other dragons mentioned in the books are:
The Cannibal - A wild dragon that was the color of coal. As his name suggests, he ate his own kind.
Caraxes - Also called the Blood Wyrm, he was a huge red dragon.
Grey Ghost - A grey white dragon, the shade of a morning mist.
Meleys - Also called the Red Queen, she was red with touches of pink and copper.
Meraxes - This dragon had silver scales and gold eyes.
Moondancer - A female dragon, she was pale green with pearl colored horns, crest and wingbones. She was as small as a warhorse.
Seasmoke - A pale, silver-grey colored dragon.
Sheepstealer - This dragon was the color of mud.
Sunfyre - This dragon was gold and pink. He was called Sunfyre the Golden, and was regarded as the most beautiful dragon ever.
Syrax - This was a yellow colored dragon.
Tessarion - Also known as the Blue Queen, she was cobalt blue and copper. Even her flames were blue.
Vermithor - Also known as the Bronze Fury, he was bronze and tan.
For more inspiration, check out my list of Direwolves in Game of Thrones.