The budding relationship between Arwen and Aragorn brings up an interesting question ... are the two related? The short answer is, well, yes. In fact, in The Return of the King, when we learn how they met and Aragorn explains who he is, Arwen's immediate response is that, "We are akin from afar." However, while their bloodlines are related, it's definitely a very, very distant connection. Elrond's brother is a man — literally a man — named Elros. With their unique family history, the brothers and their descendants are allowed to choose between either an immortal or a mortal life.
While Elrond chooses immortality, his brother opts for mortality and ends up leading a nation of men called Númenor. Over time, that nation becomes one of Sauron's chief enemies, and eventually, it's the Númenóreans who set up the two kingdoms of Arnor and Gondor. When Arnor collapses, its royal bloodline secretly survives through the Dúnedain (that is, the Rangers) and their line of chieftains, the last of whom is Aragorn.
In other words, there are dozens of generations between Arwen and Aragorn, making them technically but extremely distantly related. Considering the fact that Tolkien came from a world where English royalty was constantly intermarrying with first and second cousins, the magnitude of the distance in Aragorn and Arwen's relationship would hardly have seemed to be much of a concern.
