After the death of his older brothers, Aemon was the true heir to the throne. Unfortunately, he refused the throne. Who knows, maybe Targaryens would still be ruling if he didn't join the Watch.
My question is: Is there anybody who still remembered him during Robert's rebellion and after it? Did Robert know? He wanted all Targaryens dead.
And also: Back in season episode 1, Robert and Ned speak in the crypts of Winterfell.
Ned: It's over, your grace. Targaryens are gone
Robert: Not all of them.
Immediately after that we see a scene with Daenerys and we can assume he was talking about her. But is it possible he meant Aemon?