I think it's the Fellowship for me.
I insist on picking one, dispite being able to pick all 3 if I wanted.
I just loved it, I still remember the atmosphere in the cinema when I went to see it. People cheering, people yelling, people crying. It was just amazing. I went to see the first showing with two of my friends and we all were just in awe at how well done it was. All the actors were just spectacular and Orlando Bloom really prooved himself in his first ever role.

The Bormomir death scene was very sad, I hated how he died and teh shock on my face when he did. It's in the second of the books so when he died in the first film I was literally like =O. We all cheered in the cinema when he was fighting even with 3 arrows in his chest.
Then again when Gandalf "died" the cinema just went completely silent. The contrast between the two deaths was another amazing moment.

So yes, the introduction to the trilogy was my favorite simply for the memory.