Is it common for PhD programs to require students to have a minimum number of papers to be eligible for the defense?
Publishing papers is not a requirement in many places, but it usually depends on the specific university and graduate program. In the U.S. these things tend to vary from school to school. Sometimes research projects funded by industry prohibit the people involved from directly publishing results.

As for a world record, I'm pretty sure nobody keeps track of that. It is pretty subjective. How would you determine whether or not the paper is from your thesis rather than just being in the same field? There shouldn't be that much value in the number of papers either.