Later on I'll write up something more substantial on the mythologies of the world that do or do not feature what Joseph Campbell called the monomyth, or the fundamental hero-quest that many popular legends derive from. The short and skinny of it is that it's mostly or only found in cultures where a decent fraction of people, not necessarily everyone, were animal herders rather than hunter-gatherers, farmers, or slash-and-burn gardeners. That future post will explain why.
For now, though, it's enough to take a look at Disney's attempts to make Americans enjoy folk legends from around the world. The first was The Jungle Book, which shows a hunter boy, although because he's raised by and hunts with a pack of wolves, he's more properly put into the category of wild wolfmen from the mythology of Proto-Indo-Europeans, a group of nomadic pastoralists who are among the most successful at having spread their narratives across the globe.
Aladdin is based on a Near or Middle Eastern folktale and set either there or Central Asia, hotbeds of herding for millennia. Farther back in time, the Near East saw the ancient Semites spread their stories throughout the region and then later the world. Sometimes this wave of mythogenesis met with the Proto-Indo-European wave from the north, giving rise to hybrids like Zoroastrian and Ancient Greek legends, one of which was made into Hercules. However, the Semitic herdsmen would have been successful even with their less hybridized systems -- the three monotheistic religions of Judaism, Christianity, and Islam. Aside from Hamlet, the main influence on The Lion King were the stories of Joseph and Moses, who was not just any old hero of a pastoralist tribe but was a shepherd himself.
Pocohontas has little or nothing to do with the historical Native American figures, but is instead a garden variety fairy tale like you'd find back among the descendants of Proto-Indo-Europeans in Europe. The Hunchback of Notre Dame doesn't have a non-European hero, but there is a Gypsy babe. While Gypsies aren't herders, they are close enough -- they are nomadic, carry personal wealth and have some stratification (unlike hunter-gatherers), have a culture of honor among males and of chastity among females, are naturally gifted at music and singing, and a good fraction of the girls are of the pretty, charming milkmaid type.
What about the uber-farming society of China? Doesn't Mulan go against the claim? The first clue that Mulan is not Chinese is that she's riding a horse, and just to emphasize her non-Han status she's shown with a bow and arrow. The historical figure that she's based on, Hua Mulan, came from a Turkic-speaking, nomadic pastoralist region in the north of China, not from the Mandarin-speaking rice farmers.
Rounding out the Disney Renaissance is Tarzan, perhaps the only exception in that it idealizes a hunter in a not-so-pastoralist region of Africa. Still, his eagerness to go through the adolescent rites of passage to become a warrior -- not the self-effacing, easy-going hunters typical of foraging groups -- makes his character more like a Maasai, Nuer, or Dinka herdsman.
Like Pocohontas, The Emperor's New Groove is just a European fairy tale set in a foreign land, not borrowing Inca mythology as the basis of the story. The same goes for The Princess and the Frog. Brother Bear doesn't look like it has the monomyth in its narrative.
Starting in the 1990s, Disney went all multi-culti and tried to incorporate the stories from all the world's cultures into their movies. Unfortunately, most people's mythologies are boring -- interesting to study if you're an academic, but not the kind whose dramatic tension and compelling storytelling draw the audience in. Only groups where a good deal of the members are herders seem to be good at that, so even Disney's successes drawn from truly non-European sources turn out to be from pastoralist cultures.
If they didn't mind their movies lacking a hero's adventure, then they could have drawn from all sorts of other mythologies, whether from advanced agrarian societies like Ancient Egypt or the Aztecs or China, from small-scale gardening cultures like those of sub-Saharan Africa or the Pacific Islands, or from hunter-gatherer groups like the Bushmen. But if it's heroic excitement you're looking for, you'll have to turn to the wide-roaming, cattle-rustling cowboy bands.