After reading
davem's post, I find I must amend my view of sacrifice -- you are quite right
d, in your assesment of the sacrifices that these characters make (or do not make). I think that what I should have said is that Eowyn and Boromir become
willing to sacrifice their personal desires, rather than actually being required to do so. So that, Boromir, throughout his journey, is never willing to give up his desire for glory and personal honou -- this is what drives him to try and take the Ring. At the very end, however, he gives up this personal desire and 'repents' to Aragorn. It's not his death that is the sacrifice. Instead, he sacrifices his desire for the Ring, for personal renown, when he acknowleges that Aragorn is his true King and leaves it for him to save Minas Tirith. He does not die wanting what he has wanted all along.
Eowyn's sacrifice is much the same: it's not that she is willing to sacrifice herself for Theoden (with her death) that 'saves' her. Instead, her despair is converted to hope when she gives up, sacrifices, her personal desire for Aragorn -- and what he represents to her. It's interesting that Boromir is redeemed by accepting the person who Eoywn must give up. . . An interesting form of gender inversion???
And this is where Gollum really stands out, as he is never willing to sacrifice his desire for the Ring. He's willing to sacrifice everything except the Ring.
So with this new emphasis on sacrifice (and in light of
Lyta's and
Child's points about oaths and oath-breaking), I think I would like to move back from the emphasis that I've been placing on oaths and fealty. What I think Gollum, Boromir and Eowyn have in common is that each of them is committed to their own desires to such an extent that they are at odds with their duty -- now, this is where there's some differences, insofar as their duties are quite different. Boromir's duty is defined in terms of fealty and lordship (he should be acknowleging Aragorn and isn't). Eowyn's duty is to her socially defined role (she should be content to be a shieldmaiden). Gollum's duty is to Frodo.
So in the desire versus duty view of things:
Boromir realises and fulfils his duty at the end of his life, by repenting of his selfish desires for Rule (the Ring).
Eowyn realises and fulfils her duty with Faramir by repenting of her selfish desire for Aragorn.
Gollum fulfils (but does not realise) his duty when his desire for the Ring leads him to fall into the fire.
So in each case, their duty is fulfilled and their desire destroyed or overcome. But what does this mean? That any desire one has that is in contravention to one's duty is self-destructive and 'wrong'? That the only right desires are those that are in accord with what one is expected or supposed to do? I don't really by this, but I seem to have led myself toward a conclusion like that. . .
One Last Note:
Lyta, Kudos and wow

on your idea about the foils for each of the three in our current triad, particularly the way you have worked through the Eowyn-Arwen pairing. Seems to me that in this little pattern you've outlined we can see this desire/duty dialogue at work pretty clearly: who in the story is more dutiful, or less motivated by personal desire, than Faramir, Frodo and Arwen???