Oftentimes the Mythic and the Epic genre are mistaken for each other, and are used interchangeably, so I'll allow you to include either or both genres in your list so as to minimalize confusion. However, for those of you who don't know what these genre's are, they both have a couple of things in common:
1. The protagonist has some sort of event happen to them (fate) which leades them on a quest, where the fate of a large group of people are in their hands. (Which eliminates most other movies from the ring.)
2. There's some seemingly impossible to defeat evil that threatens this large group of people, and only the protagonist (could be a group in the instance of a mythic genre) can defeat this evil.
(Note: there would be some movies that are up in the air, because movies such as the Da Vinci Code feature a group threatened with ideaology instead of their lives)
So here's my list of favorite movies-- not in order-- in my favorite two genre's (the Epic and Mythic genres):
Braveheart
The Last of the Mohicans
The Last Samurai
The Lord of the Rings: The Fellowship of the Ring
The Lord of the Rings: The Return of the King
I suppose I'll have to insert the Two Towers in here, but I'm reluctant to do so, because of the dissapointment I experienced in the film's comparison to the first.
Dances with Wolves
Kingdom of Heaven
Gladiator
King Arthur
The Chronicles of Narnia: The Lion, the Witch and the Wardrobe
Lawrence of Arabia
And believe it or not, I've never even seen all of Ben-Hur >_>;;