Native Americans (here refering to indigenous peoples of the American continent, not just the United States) in cartoons are sometimes used for comic relief. One example of this is An American Tail: Fieval Goes West, the 1991 sequel to Spielberg's An American Tail. Alternatively, a Native American character comes in handy as a white hero's sidekick, as in The Lone Ranger.
A Native American main character is not necessarily good news either. Disney's Pocahontas portrays the Native American man as less desirable than the white man. In both Disney's Pocahontas and Dreamworks' The Road to El Dorado, the European man gains the affections of an attractive First Nations woman, despite the presence of strong attractive native men.
Although both films portray Native American men with a certain degree of dignity, both Disney's Pocahontas and Dreamwork's Chel are sexified female characters created for the white male gaze.
Disney's latest release, The Emperor's New Groove, is the first Disney full length animated feature with an adult m3le non-European human hero, not to mention the first Disney movie featuring a Native American man as the lead character. Unfortunately, the key character Kuzco is used almost solely for comic effect, and is not accorded the same dignity as other male Disney cartoon heroes like Phoebus in The Hunchback of Notre Dame or the prince in Beauty and the Beast.
Some more cartoons that portray Native American men in stronger roles (though largely supporting roles that are perhaps not completely free of stereotypes) include Mortal Kombat, Zorro, Calamity Jane and Spirit, Stalion of the Cimarron.