How many sample questions should a PMP aspirant attempt before the real exam?

I had a very good teacher from an institute, and he used to ask questions from previous chapters as a practice, and we used to prepare for the questions beforehand. On each module this practice was happening. Before we attended the exams, we had sufficient preparation with 2,500 sample question bank from which we used to prepare.

Proud to say that with enough preparation you can definitely make it. Live example is that when I used to prepare for classes during my pre-engineering days, for 10+1, we had a math class. Our teacher, after writing down the question from one text book, told all of us, that it is not possible to solve this question. But since I had visited the library and had a look at exactly the same question and how it was solved, I was able to explain to the teacher, and the teacher in turn explained it to the class. No boasting, but giving hope to those who procrastinate and may be still in the process of getting certified if it inspires.

As much as you can do, just do it but if you feel the questions look familiar then stop it. number doesn't matter.

1000 or a score on a good practice test of 85%+ correct!

It is different for everyone, but from the standpoint of someone who does not work in a PM environment, I passed the exam after reviewing ~1200 questions from two reliable sources: I answered 650 practice questions using the Pocket PMI app, and ~600 more from Andy Crowe's program. If I had had the time, I would have also reviewed another 500 questions from Rita Mulcahy's program. I found it helpful to study the answers (correct vs. incorrect) after every practice test.

I agree with all who said "it depends". Main thing is to understand first the PMI concept, then to understand the questions and what is behind the question.
I have done my preparation together with other colleagues in a learning group. In each session 1 or 2 areas were presented by a member, discussed and finished with a questionaire to the topic. At the end complete mock exams were done together. During the whole time I have done mock exams by myself with an increasing score rate.
Look for different mock exam providers, it doesn't matter if paper based, online or downloadable, but they have to be serious ones as already said.
Until now I have coached two more learning groups and adviced them to do it like this. And the first pass rate in the exams was ~95%.
As a conclusion: try to find others who are willing to prepare together, learn together, answer questions alone, exchange your results (and why you got them) and learn again.