I personally have a lot of faves. To name a few, I have to say:
1. Frodo volunteers to take the Ring to Mordor.
2. The Fellowship on the Bridge. The movie makes it so much more epic!
3. Sam faces off with Shelob. Go Sam!
4. The Battle on the Pelennor Fields. Awesome battle!
5. Frodo says goodbye at the Havens.
6. Sam keeps his promise to never leave Frodo before they embark on the quest together.