When looked at objectively, I do believe that Tolkien did make a noble attempt to include some female characters in a story form that generally does exclude women. After all, the Quest Saga is usually a setting where the men will prevail. Men went out in the world, women sat home and waited. The few novels I have read where women had to attempt a quest, the first thing the character does in disguise herself as a man, for unfortunately obvious reasons.
But when the travelers do come out of the wilderness and meet woman on their home turf, so to speak, I believe Tolkien does an admirable job of portraying them as as well-rounded, interesting characters. I think he was aided in this by limiting the romantic entanglements in the novel. Since he chose not to portray most of the women in the book as objects of a male character's affections, this meant that he had to develop the character on a more cerebral level, as advisors, councilors, or even as antagonist, as in the case of the irritating, but ultimately spunky Lobelia Sackville-Baggins.
As for the individual characters, I see Eowyn as the most complex, "human" female character in the book, and Tolkien does a good job of kindling sympathy for the restless, strong-willed girl, faced with the hopeless task of caring for a spell-entranced father figure, and the threat of an intolerable forced marriage to the evil Wormtongue. I believe Tolkien had a good handle on the dilemma that so many women through history have faced: choices dictated by the whims and wishes of the men around them, which are really not their choices at all.
Galadriel I see in the same role as Elrond: an Elder Statesman who no longer rides to the field of battle, but takes on the much more burdensome task of Leadership, commanding from afar and making the ultimate decisions concerning the fate of their people. Galadriel never comes across as a "second-class citizen". She is the equal to the greatest men portrayed in the trilogy, and the reader is never in doubt of her status.
As for Goldberry: I think Frodo was half in love with her. She represents the best of Womankind, wise, beautiful, loving, protective, and comforting. And she has an approachablessness to her that the lofty Elves and Humans never demonstrate. The more light-hearted Goldberry would definitely appeal to a Halfling's heart. Of course, Frodo is a true gentlehobbit, and would never make a move on a woman who was "taken".
Arwen seems to fall into the category that most women wind up in these novels: she who stands by her man by keeping the home fires burning. Because she is the love interest to the Hero figure of Aragorn, her role is to weave banners, write supportive letters, build her trousseau, and generally wait around for everything to settle down, so that Aragorn can finally claim her in marriage. And of course, in the end, gracefully die rather than be deprived of her True Love. Not the most exciting role to play, but hey, women always give up something for love.
I think that overall, Tolkien was great at writing how the smallest and/or "weakest" can actually become the greatest. Hobbits are another example of this. I believe that the Hobbits accomplish more than any of the Men. They are beings of a lesser greatness who become great in the end. The same goes for all of the women in the story. Eowyn overcomes her longing for Aragorn to find true love after killing the Witch King (now if that's not an accomplishment...). Arwen basically banishes herself from her own people in the end. That alone takes a great deal of courage. And Galadriel used her courage and great will-power to resist The Ring and hence return to the Undying Lands, from where she was banished. And let's not forget Luthien, who is named the greatest of the Eldar, and who is, perhaps, more courageous than all the sons of Feanor combined.
I don't think Tolkien deliberately wanted his works to appear feminist. I think that because there are fewer female characters, it makes them stand out more. I must admit that all of the Men and Elves became one big mass at one point, but the Hobbits and women always stood out among them.
Oh, and there is, of course, the infamous "Dead Mother" Syndrome, but hey, everybody does that.
2 cents.