The Germanic peoples called themselves Diutisc ("of the people"), whence "Deutsch," "Dutch," and this trope name; but they called their neighbors "Walhaz" (which originally meant a particular Celtic tribe, then broadened in scope to mean all foreigners, then narrowed to mean Latins), whence Wallonia, Wallachia, and Wales. The Diutisc didn't think very highly of the Walhaz (Martin Luther spoke of "Deutsche Treue, welsche Tücke," "German integrity, Latin faithlessness," and in modern English "welshing" is not a compliment), but they never denied that the Walhaz were human.
"Slav" derives from slovenin, "speaker", while the Slavs called their neighbors nemetsi ("mute" or "mumblers"): thus the names for Germany in most Slavic languages. (Not in Russian, though; the Russians know Germany as Germánija, from Latin Germania, but the German people are still Nemtsy.) The Persians/Iranians and Arabs got their names for Austria, Nimsa and Nimse, from nemetsi; they got the name from the Ottoman Turks, who had conquered most of the South Slavs and picked up the Slavic name for the Hapsburgs to the north.
The classical Greeks were similar to the Slavs, giving their neighbors a name that cast aspersions on their speaking skills: Greek "barbaros" meant "babbler," and it meant Persians and Middle Easterners, whose languages sounded like "bar bar bar" to the Greeks (their equivalent of "Blah, Blah, Blah"), later expanded to Celts, Tracians, Italians, Iberians and pretty much all non-Greeks. Therefore, the term didn't necessarily refer to the sorts of peoples who we think of when we hear "barbarian", but a generality of peoples among which there were highly advanced civilizations. Ironically, Romans were included in the term, but they obviously excluded their own kin when they adopted the term themselves, upgrading it to all non-Greek and non-Roman-or-Romanized.
It's widely believed that most northern Native Americans called themselves "the only real people" and their neighbors "the evil enemies," but this isn't usually true. The vast majority of tribes knew themselves by a name related to their location (Wyandot, "dwellers in the peninsula", also known as Hurons) or culture (Haudenosaunee, "people building a long house" in reference to their alliance, also known as Iroquois), and their neighbors by similar, if sometimes less complimentary, terms. There were a few tribes which called themselves things like "The Principal People" (Ani Yunwiya, also known as Cherokee, "Dwellers in the Mountains"), or even "The People" ("Inuit" in Inuktitut), and there were a few so warlike that their neighbors called them "the enemy" (Comanche in Ute; their name for themselves is "Buffalo-Eaters"); but there doesn't seem to have been any case of a tribe that did both. Most tribes that gave themselves names that expressed their superiority called themselves some variation of "The Best People", like the Cherokees (or the Chinese) — not "The Only People"; and the Inuit name for themselves is best explained by how there are so desperately few people that far north. Individual Inuit villages could, and sometimes did, end up so completely cut off from the world that they were apparently the only humans left alive; in a context like that, "the people" doesn't mean "our neighbors are subhuman," it means "we don't have any neighbors at all."
