From A Wiki of Ice and Fire
Balerion lets loose his flame. © Fantasy Flight Games
|Allegiance||Aegon the Conqueror|
|Book(s)|| A Game of Thrones (Mentioned)|
A Clash of Kings (Mentioned)
A Feast for Crows (Mentioned)
A Dance with Dragons (Mentioned)
Balerion, called the Black Dread, was one of the three great dragons of Aegon the Conqueror and his sisters, that were used to conquer much of Westeros during the War of Conquest. Balerion died some time during the reign of King Jaehaerys I, around two hundred years of age.
Balerion was the largest of all the Targaryen dragons, his teeth were as long as swords and his jaws big enough to swallow a mammoth whole. His fire was as black as his scales, his wingspan so vast that entire towns would fall under his shadow when he passed overhead.
Balerion was named after the ancient god of the Valyrian Freehold. He was born in Valyria. Balerion was one of the five dragons Aenar Targaryen brought with him when he fled to Dragonstone to survive until the War of Conquest.
He gained recognition as the 'Black Dread' during the War of Conquest, when Aegon rode him to victory and conquered Westeros. He became notorious in the battle that became known as the Field of Fire, the only time in history that all three of the fabled Targaryen dragons took to the sky at the same time. Between Vhaghar, Meraxes and Balerion, four thousand men were burned to death. King Mern died, and with him House Gardener. The army was broken and Aegon I was victorious.
Along with other Targaryen dragon skulls Balerion's huge skull used to hang on a wall in the Red Keep's throne room. After the War of the Usurper King Robert had Balerion's skull removed and stored in a dank cellar along with the others.
There is a rather nice picture of Balerion the Black Dread done in coloured inks in the book Dragonkin, Being a History of House Targaryen from Exile to Apotheosis, with a Consideration of the Life and Death of Dragons written by Maester Thomax. 
Known dragonriders of Balerion
|“||His fire was as black as his scales, his wings so vast that whole towns were swallowed up in their shadow when he passed overhead. ||”|
|“||Balerion the Black Dread was two hundred years old when he died during the reign of Jaehaerys the Conciliator. He was so large he could swallow an aurochs whole. A dragon never stops growing, Your Grace, so long as he has food and freedom. ||”|