On a personal note: listening to the piece, and thinking about the epic John Barry-esque class and style Shore has brought to the whole of The Two Towers, something occurred to me about this final cue. "Gollum's Song" sounds a lot like a Bond title song turned on its ear, probably the darkest and most somber Bond title song you've ever heard. Don't worry: there are no backbeats or anything like that, just pure, vintage creepy Shore. But you'll know what I mean when you hear it. It's fantastic, a perfect encapsulation of the malevolent yet pathetic Gollum.
That's exactly my reaction: at first I thought I was hearing a James Bond theme, then I realized that it was stranger and more original than that. Very spooky.