Aemon Targaryen joined the Night's Watch to prevent a civil war and protect his brother Egg (Aegon V)
when the Great Council of 233 AC passes over older candidates and offers him the Iron Throne directly, he refuses, already bound by his vows as a Maester. but he knows refusing once isn't enough, ambitious lords would still try to use him as a puppet to challenge Egg's reign later on.
so he takes the black on purpose, permanently stripping himself of any royal claim he could ever be leveraged with.
he gives up power, comfort, even his own family name, just so Egg can actually rule without a rival claimant hanging over him. spends the rest of his long life as a humble healer at the Wall instead of anywhere near a throne.