Aegon III Targaryen

"Rhaenyra Targaryen was murdered by her brother, or rather, his dragon. It ate her while her son watched. What's left of her is buried in the crypts right down there."

- King Joffrey Baratheon points out what little remains of Rhaenyra in the Great Sept of Baelor

Aegon III Targaryen is an unseen character in Game of Thrones. He is long dead by the time of the series. He was a King of the Targaryen dynasty.

Background
Aegon III was a King of the Targaryen dynasty. He was the son of Rhaenyra Targaryen.

Season 3
While touring the Great Sept of Baelor in King's Landing, King Joffrey Baratheon explains to Margaery Tyrell that Rhaenyra Targaryen was eaten by her brother's dragon while her son - Aegon III, whom he doesn't mention by name - was forced to watch.

In the books
In the A Song of Ice and Fire novels, Aegon III watched as his mother was devoured by the dragon of Aegon II, his uncle, during the civil war known as the Dance of Dragons. Due to the trauma of witnessing his mother's death, Aegon III developed a fierce hatred and terror of the creatures.

Aegon III ascended to the Iron Throne after Aegon II died without any males heirs. He married Aegon II's daughter (and only surviving child) Jaehaera to seal the peace between the two rival branches of House Targaryen. However, she later died without issue, ending Aegon II's line entirely. Aegon III then remarried to Daenaera of House Velaryon, who was the mother of all of his subsequent children.

Aegon III ruled the Seven Kingdoms long and well, repairing the extensive damage wrought by the civil war. Aegon III is nonetheless often blamed for the death of the last dragon, for which he became known as "Aegon the Dragonbane", despite his later efforts to obtain Dragon eggs. At some point he had nine mages cross the sea to attempt to hatch his remaining cache of eggs.

Aegon had two sons: Daeron, called the Young Dragon, and Baelor, called Baelor the Blessed, and among his daughters were the three "Maidens in the Tower," Daena the Defiant, Rhaena and Elaena. Upon his death in 157AL, Aegon III was succeeded by his young son Daeron. Aegon was said to have always walked with a great grief, and the folly of his sons nearly tore the realm apart.

Both of Aegon III's sons ruled as king but both died without issue. Aftewards, due to the new succession laws Aegon III had enacted, his three daughters were skipped over, and his younger brother Viserys II was crowned king. Therefore later Targaryens such as Daenerys do not descend from him. However, his daughter Daena had a love affair with Viserys II's son King Aegon IV, which produced Aegon IV's bastard son Daemon Blackfyre. Aegon IV legitimized him on his deathbed, after which Daemon founded House Blackfyre. Thus the later Targaryens descend from younger brother Viserys II, while the Blackfyres illegitimately descend from older brother Aegon III.