Is "not at all" still alive and doing well?

Solution 1:

I'm not sure how "Not at all" sounds in response to "thank you". I guess I'd have to hear it in context. I think I would understand it.

Some alternatives which may connote the same polite dismissal might be:

Don't mention it.

No problem.

My pleasure.

Solution 2:

It would sound a little old fashioned or formal to me. Still usable, though. (I'm in Ireland.)

It is, of course, still the standard in French and Spanish: de rien, de nada.

Solution 3:

This may be overly obvious, but in American English, saying "you're welcome" is certainly polite and standard.

Solution 4:

The NOAD reports that not at all is a polite response to thanks, but I have never heard it being used.
I heard no problem more frequently.