What I love about Fellowship most are actually the scenes in The Shire. That tranquil vision and those unending moments of elation as you temporarily live there with the hobbits are so endearing that it makes me want to live there forever.
When I saw The Fellowship of the Ring in the theater the first time, I actually got tears in my eyes during those opening scenes. Middle Earth, J.R.R. Tolkien's creation, was finally on the big screen and it looked amazing!
I wept throughout both trilogies. I'm such a mush. But yes, you're right. It was so amazing to finally behold.
There are some parts in the movies (basically Return of the King) that get me every time and I can't help but choke up a bit:
"I cannot carry the ring for you... but I can carry you"
"For Frodo"
"My friends... you bow to no one"
I almost get moved just by thinking of it.
You picked three excellent examples.
Frodo Baggins: I can see the Shire. The Brandywine River, Bag End, Gandalf's fireworks, the lights in the party tree.
Samwise Gamgee: Rosie Cotton dancing. She had ribbons in her hair. If ever I was to marry someone, it would have been her. [sobs] It would have been her!
Frodo Baggins: I'm glad to be with you, Samwise Gamgee, here at the end of all things.
LOTR is my favourite book (calling it one book as I had a combined edition) - it's the only book I think I've ever cried at the end of. The movies did an incredible job of capturing the spirit of the book, IMO. I don't even care too much about the multiple endings, or leaving out sections like The Scouring Of The Shire - I think it was fair enough that some things had to be cut to work as a movie series.
The Hobbit movies, on the other hand, didn't really recapture that magic for me.
Back on topic - the last movie I saw was Django Unchained, last night on Netflix.