From The Hobbit, through Lord of the Rings to the Tales of King Arthur and even the current Game of Thrones; there are three basic elements a story or movie needs to have to be truly an Epic Fantasy.
1. A Prophecy of a Chosen One (s)
Every great story needs to have a hero who is chosen to do some great deed or perhaps wield a great weapon of power against an impending Evil. Whether it was Frodo, chosen to carry the Ring of Sauron to Mount Doom or young King Arthur: the only one able to pull Excalibur from the stone- A chosen one is needed. In the Lord of the Rings, Aragorn returns from exile and becomes the long awaited King who will defend Gondor against the Armies of Sauron, armed with the reforged sword of his ancestor.
2. There must be a Quest.
Whether it is the Knights of King Arthur Questing for the Holy Grail or Frodo and Sam traveling to Mount Doom to destroy the Ring of Sauron, there must be a purpose for the Hero(s.) They must strive to accomplish some great mission or journey against long odds. Otherwise, the story would not be so Epic if everyone is just sitting around in a Mead Hall getting drunk and feasting alongside some buxom wenches.
3. A formidable Foe.
Whether it is the Dark Lord Sauron himself or the Evil Half-Sister of King Arthur: Morgana, The story needs a formidable Antagonist. The Hero must struggle greatly to defeat this Foe and his minions in order for there to be Peace at long last. Another great Foe was Thulsa Doom of 1982's Conan the Barbarian- a foe that Conan plotted his vengeance against from when he was a small child...
So there you have it. Three basic elements to making a great Epic Fantasy Tale. You can probably list dozens of stories or movies like this that have this working formula for success.