Ah, there are so many for different reasons. Generally, I think Tolkien described love stories very beautifully. There was always something on the background that made the affection profound and touching. For example one of my favourites is the relationship between Níniel and Túrin. As twisted and unfortunate their love is, it's sweet that two such miserable characters find a little happiness together for a while.
Then there are of course Faramir and Eowyn, those two sweethearts. One can't just help
loving their story, can one? It's probably the only affair that made me really happy for them. As Evisse said, I too when I read the book, was worrying if they will end up together (Dang it! Eowyn, can't you just fall in love already?!). And when they did, it was such a relief