I believe that the relationship between Aragorn and Arwen is a crutial part of the story as she is, in a big way, a motivator for Aragorn to succeed in overcoming The Shadow and fulfilling his birthright as King.
(Elrond to Aragorn; Appendix A) She shall not be the bride of any Man less than the King of both Gondor and Arnor.
I'm not saying this is the only reason Aragorn wanted to be King, but I'm sure it played a part.
PJ did a very good job of intertwining the stories from the Appendix with the main story from the book. And though many people scorn Arwen's extended role in the movie adaptation, I think PJ kept it at an acceptable level so as not to take away too much from the rest of the book.
The best way I can think of to explain the necessity of Arwen's greater role in the movie is:
The appendices are actually intended to be read and serve to elaborate and enrich the depth of the story; so if one were to say that the 'extra' scenes with Arwen are not really part of the story and should not be in the movie, then I would have to disagree because the events involving Arwen and Aragorn recorded in the Appendix run concurrently with the main story and give us greater insight into Aragorn's character as well as Arwen's.
Many of the scenes can be justified with a quote from the Appendix, eg: In FotR when Arwen talks to Aragorn by the shards of Narsil, giving him encouragement "you will face the same evil and you will defeat it"
(from Appendix A) 'And Arwen said: "Dark is the Shadow, and yet my heart rejoices; for you, Estel(Aragorn), shall be among the great whose valour will destroy it."
In TTT when she appears to Aragorn in a dream and when she kisses him after his near-death in the river:
and when Aragorn was abroad, from afar she watched over him in thought
I think the main reason why so many guys don't like Arwen featuring so much in the movie is because they are affraid of / or don't understand the concept of true love. I mean it's very different to the kind of love found in teen flicks and putrid, mushy romances.
As for Galadriel giving Arwen Nenya, it doesn't make sense to me because in the book she takes it with her to the Undying Lands; and now that in the end the One ring is destroyed, all the remaining rings have lost most (if not all) of their power so there would be no point to Arwen receiving Nenya. But that remains to be seen, since Arwen_Ringbearer has some inside info.
*this little elf is green with envy*