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My family lived from 1969 through 2006 in a house in Colorado with a basement. My stepmother--who grew up in a region with cooler summers--ight have perished of heat exhaustion but for the basement. What anyone in particular had outside our neighborhood, I can't say; but I think that basements were not unusual in Denver.

I've lived in Oregon, Washington, Nevada and Colorado and I've seen and lived in plenty of places with basements.

On flat land, basements are a function of home (and land) price. In places where the frost line is not very deep, a basement is a luxury. One of the most expensive parts of the house is laying the foundation, and not building a basement is far cheaper than building a basement.

If the frost line is lower, then a basement is very little extra cost since you are digging deeper and laying more concrete anyway.

If you are building on a hill, then making a 3 story house is also very little extra cost.

3/6 of the houses I spent a lot of time in as a kid had finished basements.

Anecdotally, finished basements are practically required if there is any sort of hill, which fairly common in the west, whereas they're likely to be absent for houses built on the floodplain.