In common conversation in the US Midwest I rarely hear “Not at all” or “Don’t mention it.” “No problem” is very common, and “You’re welcome” is also pretty well-used.
My personal usage:
I use “Not at all,” “Don’t mention it,” and “No problem” when the activity I’m being thanked for was really no big deal. I use “My pleasure” when emphasizing that I’m happy to be of assistance (often in a customer service context), and “You’re welcome” when the action prompting the thanks was a little bit of a bother. In essence I use different phrases to indicate how “thanks-worthy” the activity was.
That’s probably not common usage, though.
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