As I've been diving into the Lord of the Rings game, I've also been rereading the trilogy and rewatching the Peter Jackson movies from a few years back. I've just gotten to the part in the movies where Grima and Saruman have identified Aragorn's ring as the "Ring of Barahir."
Being ever curious, I decided to snoop around and find out a bit more of this heirloom, which according to the story is a mark of Aragorn's kingship.
According to the summary on Wikipedia (which is affirmed by my MERP sourcebooks), the ring has a lengthy history as an artifact of Arnor, the north kingdom of the Dunadain after the fall of Numenor.
I find that interesting, because the shards of Narsil are also regarded as an heirloom of the north kingdom.
Is it just me, or do the two most important marks of Aragorn's kingship, the Ring of Barahir and the Sword-that-was-broken, both point to him as the Heir of Arnor, not Gondor? Granted, the north kingdom is long destroyed by the events in the Lord of the Rings and also Aragorn's reign at the end of that book extends over the lands of the north kingdom. But it seems odd to people make such a fuss over these two items when they belong to the north, not to Gondor.
(Also, Elrond grants Aragorn the Scepter of Annuminas as a gift upon receiving the crown, yet another artifact of the kingdom of the north.)