Aemon Targaryen, also called Maester Aemon, was the third son of Maekar I who became a maester and a brother of the Night's Watch. He served the Watch for well over eigthy years, with the rest of the realm all but forgetting about his royal blood.
Aemon Targaryen was the second of his name, and the third son of Maekar I Targaryen. Aemon and was named after his great-great uncle, Prince Aemon Targaryen (the former Lord Commander of the Kingsguard), by his grandfather King Daeron II Targaryen. At this time, King Daeron II had four grown sons, three with sons of their own, and so felt that having too many potential Targaryen heirs was dangerous. He forged his chain, and earned the title of Maester Aemon. He served an unidentified lord until his father, now King Maekar I, summoned him to court to serve the Iron Throne. Not wanting to displace the Grand Maester, Aemon chose instead to serve at the keep of his eldest brother, Prince Daeron. After Daeron's death, Maester Aemon's whereabouts are unknown until the death of King Maekar I, when Aemon was summoned to court in the year of the Great Council. He was offered the crown, quietly, but refused, ceding rule to his younger brother, Aegon. He then decided to serve as a black brother of the Night's Watch for fear that he may be used in a plot to usurp his brother.
Maester Aemon stayed at Castle Black during the conflict with the Free Folk, providing guidance to Jon Snow and the rest of the men. During Stannis Baratheon's occupation of the Wall, the new Lord Commander Snow sent Aemon to Oldtown with Samwell Tarly and the wildling girl Gilly, smuggling out Mance Rayder's child, not her own. This was to remove all "royal blood" from the castle, so Melisandre would not be able to use them in her blood sacrifices. However, the sea voyage was too hard for the old man; he died in Braavos of a chill at the age of one hundred and two. His body was brought preserved in a barrel back to Oldtown by Sam. Gilly and Sam decided that when the baby is two years old (when wildlings are named) they will name him after the Maester, Aemon Battleborn.
He was a great-grand-uncle of Daenerys Targaryen, who he never met during his life, but heard rumors about shortly before his death. He was convinced that she was the Prince that was Promised, as the Valyrian word for "prince" is actually gender neutral.