In my highschool art class one of our assignments was to paint a still from one of our favorite movies. It was a great exercise!
One of my favorite live action movies as far as composition goes (and, well, I love the story too) is Fiddler on the Roof. There are so many shots with amazing composition in that one. I watched it and paused it to do a quick value study periodically and I was seriously pausing it every few seconds it seemed like! It did win an Oscar for best cinematography, I believe, and it was well deserved.
Also if you're into romances, the new Pride and Prejudice (the one with Keira Knightley, not the zombies one 😉 has some awesome composition shots as well. Plot-wise I prefer the A&E long version, but I can sit through the new short version because it's just so pretty ;-).