I would guess that native women who did not interact with European culture did not wear them, but were there any countries within Europe that did not adopt the fashion? Or groups of women (for instance: the handicapped, the very poor, perhaps women settlers in North America) who didn't wear them? I'm curious, I guess, about their inception and if any women refused to wear them or were unable to.
The corset that we think of evolved as an undergarment throughout history. In the 16th and 17th centuries you would read references to the stomacher, and in the 18th century to the pannier. Corsets changed during the Regency Era of the early 19th century the fashionable look was the natural, classic greek form, with the tell-tale high-waisted dresses. At that time the corset went from conforming the torso and waist (think late 18th century dress with the wide panniers), to having it's purpose change to just providing a support for the bust. There were several corset options at the time, including a short version that is no longer than a bra would be today. The corset at that time could be used to slim the waist, but that wasn't it's primary purpose.^[1]
There was a corset controversy in the mid-late 1800s when tight lacing and tiny waists became very popular. It was controversial, with many (men and women) pointing out that it could not be healthy for one's internal organs. ^[2]. I know that using wikipedia as a source is not acceptable, but I would like to point out that there is a Wiki article about the corset controversy, which links to several primary sources on the subject.