Kili and Tauriel? Aragorn and Arwen? Faramir and Eowyn? Sam and Rosie? Galadriel and Celeborn? This should be an easier choice, considering how few couples there are in these movies. We barely meet Celeborn or Rosie, so those are kind of out. Faramir and Eowyn get a bit of development as a couple in the extended editions, but barely enough to count. Which leaves me the choice between Kili/Tauriel and Aragorn/Arwen.
The funny thing is, this shouldn't be hard either. Because Tauriel and Kili are two of my favorite characters, and Aragorn and Arwen don't make the list. So clearly, I should be team Taurili (Kiliel?). And I am, in that I ship them and not Legoliel (Taurolas? I'm not good at the whole name-combo thing). But their relationship barely gets started -- they get some cute chats and a few meaningful glances, and then a sad ending. They don't get to know each other, that we see, and their only opportunity to do so would be while Tauriel's helping nurse Kili back to health at Bard's house. And Kili's feverish or unconscious most of that time. If Kili had lived, if they were able to go away together and find a place in the world where a dwarf-elf relationship would work out, then I would choose them. But that doesn't happen.
So, surprise, surprise! My favorite couple is Aragorn and Arwen.
And really, that makes a great deal of sense. I love May-December romances, and Arwen is ever so much older than Aragorn. I love romances between people who have known each other for years, who grew up together and then fell in love, and that's obviously the case for them. And I love romances where they have to defy odds or conventions or some kind of opposition to be together. Elrond opposed their marriage for a long time because he doesn't want Arwen to eventually experience the grief of losing her husband. Arwen has decided the joy of their years together is worth the pain of eventual separation, and I heartily applaud her for both disagreeing with her powerful father, but also for initially obeying him, and slowly helping him change his mind rather than outright disobeying and opposing him.