Arwen and Aragorn's romance is important to the story of LOTRs

I rather commonly see people saying it is not, criticizing the Peter Jackson films for giving so much screen time to an unimportant side story for the sake of making the movie less of a Sausage Fest.

The Lord of The Rings trilogy of novels are not structured like most novels.  They are six prose narratives and a collection of Appendices published in three volumes.  A lot of important scenes are in the books revealed as flashbacks, which adaptations tend to show when they actually happened, like Gandalf going to Isengard where Saurman reveals his betrayal.

So yes, in the proper narrative of LOTR, Arwen appears in only a few scenes.  However Aragorn also comes off as a pretty one dimensional character in that proper narrative.

The Appendices reveal the history between Aragorn and Arwen, and it becomes clear his Love for Arwen is the primary thing that was driving him.  A fact that was talked about in the special features of the DVDs for the films.

Tolkien wanted Aragorn and Arwen to be as important as the Man+Elf Maiden pairings of the First Age, the first of which was Beren and Luthien.  So I really get annoyed at supposed fans of Tolkien diminishing it's importance for the sake of criticizing a trio of movies that yes, took a lot of inevitable liberties, some I'm more fine with then others, but overall they were perfectly enjoyable films.

The previous adaptation of LOTR, the Ralph Bakshi animated movie, also replaced Glorfindel in his role in the journey to Rivendale.  Since Glorfindel doesn't appear again in the main narrative, (given the continuity issues his presence in LOTR causes I suspect Tolkien picked the name at random).  So replacing him here with someone more important to this narrative is a perfectly valid decision.

The Bakshi film replaced him with Legolas, which bugs me only because I feel Legolas, Gimli and Boromir should all be introduced at about the same time, the Elf, the Dwarf and the Gondorian of the Fellowship.  So Jackson's decision to use this opportunity to introduce Arwen is a far better decision in my view, and her Bad@$$ moment in the movie helps make her a more worthy successor to Luthien, who defeated Morgoth.

Now the Hobbit films' approach to providing more female presence was much more questionable.  I enjoyed Tauriel, but the actress originally took the role being promised there wouldn't be a shoehorned in romance, then they changed that on her.  What bugs me most though is how in the final battle scene she ultimately gets sidelined for Legolas to take the most impressive action again.  I wish she had killed the Orc who killed Kili.

Arwen in the LOTR films I think was handled perfectly fine.