Ignatius Donnelly had this diagram from his book Atlantis: the Antediluvian World in 1881. The upper dotted line curve presumes to show the profile of the undeformed cranium, the lower ones are different crania from around the world. The uppermost curve is not directly aligned with the others because it was intended to be shown clearer. Donnelly was seeking to demonstrate that the idea of cranial deformation originated in a set of peoples whose heads already tended to be shaped that way, and the deformation was then done to accentuate the natural trait. The photo is an undeformed skull from early Crete: skulls from North Africa and the Canary Islands, as well as from Pyramid-builder's cemeteries in Egypt and also in the Near East, all tended to this pattern.
Neolithic deformed skull from Palestine, prepottery period, probably about 8000 BC. The trait is earliest in the preceeding Naftufian period, just about at the end of the last Ice Age. Contrary to some reports, Neanderthal skulls were not artificially deformed (they grew that way naturally) but some of the CroMagnon skulls were, including one of the skulls found in the original excavations at the Cro-Magnon cave itself (Cro-Magnon means "Great-Big" in France; it originally meant the cave was big itself but since CroMagnon people were also tall, the name was appropriate)
Early-Neolithic deformed skull from Iran, Wikipedia image: these skulls are common from about 5000 to 7000 BC in the areas that would later become Iran and then diffusing out into the surrounding territories. Many skulls in the same time period from Iraq, Southern Turkey and Syria are also deformed but not usually so severely. In later historical time many of the Iranian-speaking nomads of Central Asia continued the tradition and eventually the trait was introduced into Europe from the East by the invasions of the Huns.
These are some more Hun skulls, recently several such skulls were discovered in Siberia
Types of artificially deformed craina found in the Eastern United States from a recent article by Neumann. Many of the same styles of deforming the skulls of the infants also occur in South America. The skull illustrated at center-top is undeformed and normal, shown for comparison. Infant showing the effects of cradleboarding in a modern medical context, and below, the cradleboard in use, with the babby wrapped in swaddling clothes. Which can probably be compared to mummy wrappings and probably came from the same parent culture that invented mummification. The Cradleboard in this case is Navajo and one of the local lambs has gone to inspect the baby.