Is a question like
What is your favorite pasuk?
or
What city did your grandparents inhabit in Poland?
appropriate for the site?
The argument against would be that, although such information could be of Jewish interest, neither is not the type of question that can be answered with a fact or a finite set of facts.
These questions fall outside the intended use of a Stack Exchange site. Our system is set up to handle objective questions where there is a concept of a right answer, or even a better answer. In the questions you used as an example, every question submitted would be equally correct.
I would encourage you/everyone to read the following links which explain this philosophy. The How to Ask entries also contains links in the sidebar to blog entries that I strongly recommend reading.
For new questions, I would absolutely consider the above and act accordingly.
For existing questions that were brought over from mi.yodeya, that is tougher, and something the community can figure out as is necessary. Leaving the questions means they become broken windows and new people may seem them and think it is ok to ask new questions like that. That isn't to say that priority one should be going through and finding all of these questions with a sense of urgency and deleting them. If they in some way make the internet a better place, they should be grandfathered in in some way - up to the community. Perhaps locking the question with a comment explaining why?
(Those of you familiar with Stack Overflow will understand this as the rules about poll questions have changed over time and there are many existing questions from before the change still on the site.)
