I'm not vouching for all industries, but I know that in the software field having an accredited degree is more of a "oh that's nice" than a requirement to success. I've met a ton of people with no official post high school education who have been quite successful coding (turns out the school of hard knocks + internet access == all you need).

That said, I'd prefer to know that the dentist drilling into my skull has some official qualifications for doing so. Everything is a matter of degrees....