Arwen's role inthe books was so tiny that she's not even considered a supporting character as much. We see her four times in all nine hundred-something pages. The first time was at Rivendell, during the Feast and later singing a hymn to Elbereth in the hall of fire. The second time is riding to Gondor and marrying Aragorn after he becomes King. The third time, she's singing in the castle courtyard, and speaking quietly with Frodo. The fourth, and final mention of the Evenstar in the book is her heart-wrenching farewell to her father at Rivendell. Thus the story turns, full circle.
Some people have foolishly said that if Arwen wasn't even there at all, it wouldn't have changed a thing. Extremely wrong on their part. Think about it. It all started with Aragorn and his falling in love with her. If he hadn't met her, he would never have set off on his journey to make himself worthy of her, he would have never met Gandalf, the Fellowship would be without him (and probably failed, that is, if the hobbits even got out of the Prancing Pony alive...), Gondor would fall, the Kingdoms would never be reunited, so on so forth. Wreckage and ruin for all. Arwen is more or less the catalyst of all of Aragorn's events, and is, without a doubt, the foundation for the success of the Quest.
And if, despite all this, the Quest did suceed, there would be no place on the boat to Valinor for Frodo. The result? Frodo probably would have continued suffering, and not long after would have died. (I don't know about you, but I'm not fond of that idea at all.)
In the movie, Arwen's role is more or less the same, except there's more ties with the Ring-bearer. She take the place of Glorfindel and rides across the Ford of Bruinen with dying Frodo, defies the Nazgûl, and causes the Fords to rise up in anger against the wraiths (instead of Elrond and Gandalf). She and the Ringbearer shared a heartwrenching moment at the Ford, when the danger had passed. Holding the deathly ill hobbit close to her and weeping, praying that her life be given to him, to let him be spared. Even if it never happened in the book, it was one of the sweetest moments Arwen had in the movie.