Arwen was a distant relative of her husband Aragorn. Aragorn's ancestor, Elros Tar-Minyatur, the first King of Númenor, was her father Elrond's brother, who chose to live as a Man rather than as one of the Eldar.
Arwen's grandfather is Earendil half-elven, ancestor of Aragorn. By my estimates from reading the Akallabêth, Aragorn is approximately 64th in line from Elros Minyatur, making him Arwen's first cousin, 63 times removed.
Are Aragorn and Arwen cousins? Yes. Aragorn is a direct descendant of Elrond's brother Elros, who chose mortality and became the first King of Numenor. So Aragorn and Arwen are first cousin approx.
Because Aragorn is mortal and Arwen chose to remain in Gondor and become mortal, their son, Eldarion, is mortal as well, despite his Elven lineage.
They are both elvish nobles, as Legolas is the son of King Thranduil and Arwen is the daughter of Elrond. They are both well-educated and would have known each other as the community of elves is quite small. It's likely they would have been at least friendly with one another.
The actor is suffering from Legolas Syndrome — where you accidentally get cast into a role that suits you far more than your real-life looks, leaving you with a tricky predicament after the wrap party.
It is later mentioned that Tauriel is a talented warrior and was therefore made leader of the Mirkwood border guards. Legolas, the son of Mirkwood's Elven king Thranduil, is indicated to be attracted to her, but as she is a lowly Silvan Elf, she does not believe herself worthy of him.
Elrond has only Half-Elf, and he was once given the choice to be counted among Man or Elves. When he chose to be counted as Elven kind, he was then given immortality. Because Arwen is Elrond's daughter and also Half-Elf, she too has the choice to be a mortal woman or an immortal Elf.
And after their marriage, both Aragorn and Arwen are mortal. Arwen, therefore, could not set foot in the Undying Lands without special permission. And she wouldn't be likely to go after it in the end. So unfortunately, she would not go there, unlike Legolas, after Aragorn's passing.
Originally, Tolkien intended for Éowyn to marry Aragorn. Later, however, he decided against it because Aragorn was "too old and lordly and grim". He considered making Éowyn the twin sister of Éomund, and having her die "to avenge or save Théoden".
Arwen didn't want Aragorn to die, because if he died so would she. She said she wasn't tired of living yet. But instead, Aragorn chose to die and Arwen lived a year longer before dying herself.
The Tale of Aragorn and Arwen, an appendix to the main story, relates that Aragorn and Arwen had a son, Eldarion, and at least two unnamed daughters. One year after Aragorn's death, Arwen dies at the age of 2,901.
Technically, Arwen is Aragorn's aunt, but it's not as weird as it sounds (at least within the context of Middle Earth). The romance and marriage of Arwen and Aragorn are unique in a variety of ways.
Legolas and Arwen in Rivendell
These two elves aren't actually seen together at any point in the trilogy, but they do in fact have a strong sense of kinship, which can be seen in one of these unused clips where Legolas arrives in Rivendell and Arwen and a host of other elves are there to meet him.
Aragorn and Boromir, unrelated by blood but united in their love of Gondor, were the only two men who set out with the Company from Rivendell.
When they meet, Arwen is thousands of years old with immortal beauty and he a young 20-something man. However, next time they meet, Aragorn is in his 50s. This was when Arwen fell in love with him, so his 30 years of maturing must have done some good. Aragorn eventually would live to be 210.
At this point Arwen has already given up her immortality, but now she grants the grace of the Eldar to Frodo, not giving him immortality since he is not one of the elves, but instead granting him a home in the undying lands when he does pass.
In the year 121 of the Fourth Age, after Aragorn's death, Arwen died of a broken heart at Cerin Amroth in Lórien, and was buried there one year after the death of Aragorn, to whom she had been wedded for 122 years. She was 2901 years old.
She was captured and tormented, receiving a poisoned wound. Her sons rescued her and she was physically healed by Elrond, but never fully recovered in mind or spirit, and no longer wished to stay in Middle-earth. She left for the Grey Havens and passed over the Great Sea the following year.
She has a vision of a child clothed in white running across her path. She watches as the boy runs with his arms outstretched to his father, an aged Aragorn, who picks him up with joy and kisses him. As the boy looks at her and she sees he is wearing the Evenstar, she knows the boy to be her child.
Legolas is an elf, so he is immortal. However, he is only immortal in the sense that he will never die of old age or sickness. He can die in battle.
Partially this was due to the unique situation of their ancestry: because of the complications of being descendants of marriages between mortals and immortals, Elrond and his brother Elros were given the choice of their own fates, to be mortal with humanity or immortal with the elves.
Legolas does not marry or have any children, based on the appendix of The Lord of the Rings. Regardless of who his mother was, Legolas is the last of his line. When he sails into the West at the beginning of the Fourth Age, he leaves no family members behind.
“You gave me a very special bow, and I look after it.” In related news, sources reveal that I “had such a crush” on Aragorn, son of Arathorn, called Elessar, the Elfstone, Dúnadan, the heir of Isildur Elendil's son of Gondor.
He Only Speaks To Frodo Once
Given all of that, you would think that Legolas would have more than a passing acquaintance with the Hobbit. In fact, the two of them only spoke once in the entirety of Peter Jackson's trilogy.