Are there some programming questions
considered to be an absolute
must-know-the-answer for someone to be
a good programmer?
I think yes. Possibly the more relevant question is like
Are there some programming questions
considered to be an absolute
must-know-the-answer for someone to get
hired in an interview?
which is I think a stronger yes. If you're interviewing in my office, and I ask you to write code on the whiteboard to sort an array or a list, and you can't do it, then my hunch is you are not a good programmer, but more importantly, there's no way I'm going to hire you.
The implicit followup question: ok, if such questions exist, which questions are they? They are the popular ones about lists and arrays and trees and parsing and calculators and all those little problems you find on the web that have code answers of 25 lines of code or less and are relatively language-agnostic. (They are not the boring specific minutae like 'what happens in C++ when you delete null?')
If you find yourself having trouble with some of these 'popular' questions, then go spend some time on a Saturday and solve them! You might learn something. And even more likely, you might be better prepared for your next interview, whenever that may be.
(my rambling opinion)