Lovely post, Inziladun.
Aragorn was indeed an exceptional man. Frodo, Sam, Merry, Pippin, rest of the Fellowship, and the Gondorians loved him so dearly. Èowyn's love was romantic for him. Though, it did not cause her to go mad for him "that way". She loved him purely, not caring about her own feelings. That's why, after being 'neglected'(for that lack of a better word)she thought of dying.
Frodo and Sam's love has lots images in my mind. It is not only brotherly love that I can think of. There's much more. Sam not only loves Frodo, but he worships him. Frodo, like Aragorn is loved by others immediately. Be it Sam or the rest of Fellowship or even Gollum, they love him dearly. Sam loves him as a parent loves him child or a child loves his parent. As an ordinary person loves God. Their love is all but romantic.
Tolkien's work is so powerful because of devotion, respect and love that these characters have for each other!