Aerys I Targaryen is an unseen character in Game of Thrones. He is not expected to appear in the series, being long dead by the time it begins.
Aerys Targaryen was the first of his name to sit the Iron Throne and the thirteenth King of the Targaryen dynasty. He was the son of King Daeron the Good and Queen Myriah and succeeded his father after he perished in the Great Spring Sickness. Per the Targaryen tradition, he took his own sister Aelinor as his wife. His other brothers were Baelor, Rhaegel, and Maekar, who would succeed him on the Iron Throne
Aerys, along with his brothers and sister, is mentioned in the House Targaryen's entry of the book The Lineages and Histories of the Great Houses of the Seven Kingdoms.
In the books
In the A Song of Ice and Fire novels, Aerys I Targaryen is described as bookish. He was spindly and stooped, with long, straight hair. He had a long, thin face, a long, thin mustache and a long pointed beard. He inherits the Iron Throne after the Great Spring Sickness takes not only his father Daeron, but also his nephews Valarr and Matarys, the sons of his elder brother, Prince Baelor "Breakspear", who had perished defending Duncan the Tall in a Trial of Seven - a particular form of trial by combat.
Aerys appointed his uncle Brynden Rivers as Hand of the King and left the governance of the realm to him, while he occupied himself with the study of books and lore. He also shunned the bed of his sister-wife Aelinor. During this time, no one great disaster befell the realm, but it was beset by numerous minor problems which were allowed to flourish all at once due to Aerys I's inept reign. Following the great plague which killed Aerys I's father, the realm suffered a great drought, leading to famine even in breadbasket regions such as the Reach. This instability led to a great proliferation of broken men and highway robbers, and the roads were not considered safe to travel. Meanwhile, the pretenders of House Blackfyre who had fled across the Narrow Sea remained an ongoing threat. There were as many as five Blackfyre Rebellions in all, the first and greatest being the first, which occurred during the reign of Aerys I's father. Even so, the surviving Blackfyres were continually plotting new intrigues and rebellions to take the throne back, leading to the short-lived Second Blackfyre Rebellion which occurred three years into Aerys I's reign. In addition, the Lord of the Iron Islands, Dagon Greyjoy, took advantage of the chaos of the spring sickness and the Iron Throne's preoccupation with the Blackfyre rebels under Bittersteel, and raided Fair Isle, the Arbor, and even the North. Other localized rebellions of opportunity popped up throughout the kingdoms trying to take advantage of the general instability, including a revolt by the island of Skagos against Winterfell, and an attempt by the wildlings to invade south of the Wall by a new King-Beyond-the-Wall. Aerys I is overall remembered as a weak, absentee-king whose time on the throne was marked by plague, famine, Blackfyre intrigues from the Free Cities, ironborn raiding, wildling invasions, and other localized rebellions.
After Aerys' death, his brother Maekar inherited the throne, as Aerys had no heir, and their brother Rhaegel was considered crazy.
- Aerys I Targaryen at A Wiki of Ice and Fire (spoilers from the books)
Kings of the Seven Kingdoms
Aegon I, the Conqueror · Aenys I · Maegor I, the Cruel · Jaehaerys I, the Conciliator · Viserys I · Aegon II · Aegon III, the Dragonbane · Daeron I, the Young Dragon · Baelor I, the Blessed · Viserys II · Aegon IV, the Unworthy · Daeron II, the Good · Aerys I · Maekar I · Aegon V, the Unlikely · Aerys II, the Mad