Arwen Evenstar (daughter of Elrond and sister to Elladan and Elrohir) certainly stands by her man. When Aragorn settles in to become king of Gondor, she arrives at Minas Tirith ready to live a mortal life, and that's something that only one other elf woman, Luthíen Tinúviel, has ever done.
Arwen clearly adores Aragorn. After all, when Aragorn is about to march into war, she stitches him a jeweled banner that he flies from the mast of the black ship he has captured from the Haradrim. Embroidering by hand takes a lot of work (trust us, we've tried), so we're struck by Arwen's dedication. But we don't have a ton of access to Arwen's inner thoughts and feelings. In fact, her love story with Aragorn mainly comes out in the The Return of the King appendices (see Appendix A, section v).
Mostly, Arwen appears as a lovely face and not much else in the novel itself. She is generous (since she gives Frodo her seat on the elvish ship to the West) and loyal (witness her choice to stay with Aragorn in Middle-earth, even if it means ditching her dad). But she does not have Éowyn's depth or complexity as a character. We hate to say it, but we will: movie Arwen comes off much better than book Arwen. Her desperate ride with Frodo to escape the Ringwraiths is one of the most thrilling things in the film of The Fellowship of the Ring.