On the contrary, History is nothing if not a story of conquest but the European peoples have been relatively tame in regard to "destroying" other peoples, actually (the North-East Asians seem to be even more tame but they also produced the Mongols of Genghis Khan). The Vikings, that you mention, did not displace any other peoples, pillaging they did (and mostly against other White Europeans) but that is relatively common form of human tribal behaviour, and they were mostly absorbed by the locals wherever they settled: in England, their genetic footprints remain to this day, I personally have a Scandinavian paternal genetic line (haplogroup I) and it probably goes back to the Viking settlements in England, but any distinct Scandinavian group ceased to exist in England long, long ago. The same is true for all the other groups that were assimilated in the various native British ethnic groups throughout the ages, indeed Europe in general has been a "melting pot" of sorts between the various European tribes throughout history.
You're in for a real treat if you believe in that whole "noble savage" nonsense. Hunter-gatherer groups (including your beloved Amerindians) commonly engaged in tribal warfare and often the denouement involved the slaughtering of all the enemy tribes males, with the sexual enslaving of the captured women. Indeed this all too human behaviour has been consecrated as holy by the great religions. Jared Diamond, a scientific hero of the political left who you'd no doubt admire, is rather honest here in his description of the nature of the tribalism of the ancient Israelites here in this book review:
"The Bible, especially the Old Testament, is full of exhortations to be cruel to heathens. Deuteronomy 20:10–18, for example, explains the obligation of the Israelites to practice genocide: when your army approaches a distant city, you should enslave all its inhabitants if it surrenders, and kill all its men and enslave its women and children and steal their cattle and everything else if it doesn't surrender. But if it's a city of the Canaanites or Hittites or any of those other abominable believers in false gods, then the true God commands you to kill everything that breathes in the city. The Book of Joshua describes approvingly how Joshua became a hero by carrying out those instructions, slaughtering all the inhabitants of over four hundred cities. The book of rabbinical commentaries known as the Talmud analyzes the potential ambiguities arising from conflicts between those two principles of "Thou shalt not kill [believers in thine own God]" and "Thou must kill [believers in another god]." For instance, according to some Talmudic commentators an Israelite is guilty of murder if he intentionally kills a fellow Israelite; is innocent if he intentionally kills a non-Israelite; and is also innocent if he kills an Israelite while throwing a stone into a group consisting of nine Israelites plus one heathen (because he might have been aiming at the one heathen)."
Here is a rather more interesting comment on his experiences with the natives of New Guinea
"Interestingly, among New Guineans, religion is never invoked to justify killing members of an out-group. Many of my New Guinean friends have described to me their participation in genocidal attacks on neighboring tribes. In all those accounts, I have never heard the slightest hint of any religious motive, of dying for God or the true religion, or of sacrificing oneself for any idealistic reason whatsoever."
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The Prophet Mohammed, after defeating the Jewish Banu Qurayza tribe (who had betrayed him in a religious-tribal war, although I think any impartial observer might have expected that given Mohammeds incessant fanatical attempts to convert them), had all the males beheaded and the females taken as *** slaves, for example (Sahih al-Bukhari, 5:58:148). Arabic and Islam originated in a small corner of the Arabian peninsula; however, the Middle East and Northern Africa were once teeming with various Semitic, Indo-Iranian and other peoples and their cultures and languages. But today Arabic and Islam cover a continents worth area of that region, what do you think happened to all those peoples, their cultures and their languages?
The Abrahamic religions are not unique in their consecration of tribal warfare and tribal genocide. Hunter-gathers like Amerindians had their religious forms of genocide too, there are many anthropological accounts of Native American tribal warfare, I will indirectly describe just one for brevity. The great Biologist E.O. Wilson very eloquently describes one such case of the Mundurucu headhunters:
"War can be defined as the violent rupture of the intricate and powerful fabric of the territorial taboos observed by social groups. The force behind most warlike policies is ethnocentrism, the irrationally exaggerated allegiance of individuals to their kin and fellow tribesmen. In general, primitive men divide the world into two tangible parts, the near environment of home, local villages, kin, friends, tame animals, and witches, and the more distant universe of neighboring villages, intertribal allies, enemies, wild animals, and ghosts. This elemental topography makes easier the distinction between enemies who can be attacked and killed and friends who cannot. The contrast is heightened by reducing enemies to frightful and even sub* human status. The Mundurucu headhunters of Brazil made all these distinctions and in addition literally turned their enemies into game. The warriors spoke of the pariwat (non-Mundurucu.) in the same language ordinarily reserved for peccary and tapir. A high status was conferred on the taker of a human trophy head. He was believed to have attained special influence with the supernatural powers of the forest. Warfare was refined into a high art, in which other tribes were skillfully hunted as though they were packs of especially dangerous animals. The raids were planned with great care. In the cover of the pre* dawn darkness the Mundurucu men circled the enemy village, while their shaman quietly blew a sleep trance on the people within. The attack began at dawn. Incendiary arrows were shot onto the thatched houses, then the attackers ran screaming out of the forest into the village, chased the inhabitants into the open, and decapitated as many adult men and women as possible. Because annihilation of an entire village was difficult and risky, the attackers soon retreated with the heads of their victims. They proceeded on forced march as far as they could before resting, then headed home or on to the next enemy village." (On Human Nature, pages 110-111).
So you see, tribal genocide has often been practiced as a holy ritual throughout history by a lot of peoples, one thing that the European peoples at least did not do (the crusades were more mutual). Moreover, European peoples have actually been mild in imposing their own languages and cultures on other peoples compared to say, the Arabs and Muslims.
Finally, I think you do not understand the idea of genocide. See the holocaust is an example of an attempt at genocide: a deliberated attempt to "wipe out" a peoples from existence. Could you please explain to me how the Indian Removal Act was supposed to achieve that? I never said that Amerindian were not displaced from some of their lands, what I asserted was that there was no attempt to "wipe them out" as some of you have falsely claimed here. So Ill wait for that evidence again.