My answer, originally published on Quora.
I've worked with dozens of software / online service companies and helped them recruit product management candidates. None of them care about the PMI certification, and in fact it might be seen as a sign that an applicant does not understand that the Product Management role is not ProJECT Management.
There are other ProDUCT Management Certifications out there, but they are not that common and many of the best candidates do not have them. The most important things are experience and demonstrated aptitude and passion for products. That said, the Pragmatic Marketing Certification is perhaps the most well-known certification, and I have seen it give a candidate an edge in a recruiting process, but only if all other factors are equal.