Baelor 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.
Prince Baelor, along with his family, is mentioned in 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, Prince Baelor was the eldest son of King Daeron the Good and Queen Myriah, and named after Baelor I. He had the dark hair of his mother, Queen Myriah, which he kept it cut short and kept his jaw clean-shaven. His nose had been broken twice. He was known as "Baelor Breakspear" and was the father of Princes Valarr and Matarys Targaryen.
When the Blackfyre Rebellion was in its early stages, Prince Baelor advocated leniency toward Daemon Blackfyre, a position that was rejected in favor of his uncle Brynden Rivers' hard line. Nonetheless, Baelor accepted the path towards war and distinguished himself by leading the Dornish-Stormlands force which attacked the rearguard of the rebel army during the Battle of the Redgrass Field, smashing them against the shield-wall of his brother, Prince Maekar, and inspiring the song The Hammer and Anvil. After the battle, he was named Hand of the King by his father. At some point he was also given the title of Protector of the Realm.
- Baelor Targaryen at A Wiki of Ice and Fire (spoilers from the books)