I've found that children's films are often some of the best examples of the Hero's Journey, so I'd like to take, as my first example of the Monomyth in film, Kung Fu Panda (the below does contain spoilers):
While the movie doesn't contain all 17 stages of Campbell's Monomyth, very few stories actually do.
Our hero, Po, starts off working in a noodle shop for his father who, while Po is a panda, is actually a goose. His dream is to be a great kung-fu warrior, but they are just noodle folk. "Broth runs in our veins," as his father tells him. This is Po in his Mundane World.
The Call to Adventure: An announcement comes that the Dragon Warrior will finally be chosen, the great hero who will receive the Dragon Scroll and learn the secret to unlimited power. This is Po's Call. He eagerly rushes to the temple to see the Dragon Warrior be chosen, and is, seemingly by accident, chosen himself. Despite his own shortcomings and the initially dismissive attitudes of Master Shifu and the Furious Five, Po stays, encouraged by Master Oogway's words that "There are no accidents."
Crossing of the First Threshold: The moment when the hero enters into the world of adventure and the unknown. Typically, this is where the hero meets the Threshold Guardian. In this case, it is when Po trains with the Furious Five, trying to prove that he is worthy of learning kung fu. This of course leads to...
The Road of Trials: This is the struggle to learn the lessons needed to overcome the threat. In keeping with mythic tradition, Po does fail at times, particularly in his physical training. He does, however, succeed in winning the friendship of the Furious Five, except for Tigress, anyway, and in helping Master Shifu find a way to train him. Using his stomach.
Supernatural Aid: The always-important mentor figure, in the form of Master Shifu. While Master Shifu is reluctant to train Po, it is his own mentor, Master Ooogway, and Po's own determination, that convince him to find some way to train him. It is Master Shifu who later presents Po with the Dragon Scroll, his "talisman" to give him the power to defeat the villain, Tai-Lun. However the scroll is blank. It's nothing but a sheet of reflective parchment.
Atonement with the Father: Dejected, with the Furious Five defeated and seemingly no way to defeat Tai Lun, Po returns home, jeered by the villagers. To cheer him up, his father explains the secret of his Secret Ingredient Soup: There is no secret ingredient. If you want something to be special, it will be, because people will want it to be special as well. This revelation leads Po to...
The Ultimate Boon: Po realises something no-one else can. There is no secret to unlimited power. The power is in each person. All it takes is belief. With this knowledge, Po is able to defeat Tai Lun and become the hero he always wanted to be.
There is no charge for awesomeness
Master of Two Worlds: Cheered by his fellow villagers, and receiving respectful bows from the Furious Five, Po is finally accepted in both the Mundane World and the world of kung fu.
And there we have it. Po's journey through Kung Fu Panda in terms of the Monomyth. Of course, his journey is not complete, and there are still challenges that he has to overcome in Kung Fu Panda 2, but we'll come to that another time.