Watched the extended editions back to back in one sitting (with my girlfriend, I swear I have one).
As a stand alone film (which is the only way to do this really) the Fellowship is casually the best of the 3.
The world is almost entirely set up, we see the utopian innocence of the Shire as the perfect example of what is at stake when we see the shots of Mordor and the Mines etc.
Every - very nearly every - theme in the films is shown adequately to brilliantly in the first. More is said in the first in subtext, imagery and theme than the other two combined.
You may find Frodo and his quest boring compared to (the clearly awesome) Helm's Deep and Minas Tirith, but make not mistake about it, that is the main thrust of all the films. If Frodo fails and the ring returns to Sauran, then all the wacky human shit doesn't really matter. Stuff like the King burning his son alive is tame compared what is at stake at the point in RoTK.
The first one is the only true quest, thrust onto an unsuspecting and harmless hobbit with whom we're clearly supposed to identify. Forced away fro home for the first time with a few friends, into the unknown and the dangerous. Taken through varying terrain and places to never get bored, every single place incredibly beautifully shot (not that other two weren't, just that there were more examples of incredible cinematography in the first).
His quest gets ever more dangerous (as it should) until in the midst of battle he decides to do the last stretch himself (along with Sam). The films end there, or could. Admittedly on a heavy cliffhanger, but we see no enemies on the other side of the mountains, and however much you may like Mari and Pipin (sp?) their fate just doesn't matter all that much.
I will say that the second two comfortably make it vastly more epic, by establishing new characters and backstory to existing ones. The battles themselves getting steadily greater.