Well, since we're all chiming in...
I don't consider myself a professional programmer either. Although I do write programs occasionally. Some of the coding I do is for work. Some is just for me. I write things to save time or to fill a need. Most of the time I'm an Oracle DBA. At least that's been in my job description for most of the last decade.
I'm one of the types of people that professional programmers work with on a regular basis. As far as schooling goes, I can tell you that people end up as programmers with all kinds of educational backgrounds. You have your computer science types and you also have your astronomy(or whatever) majors turned computer guy/gal. You have people with BS degrees and people with MS degrees. You have people with no degrees at all. A lot depends on the organization and what Human Resources has been told the educational requirements are. Personally, I think a degree of some sort gives you a better foundation in the long run and offers more flexibility when finding employment. If you enter the field without a degree, work for someone who'll pay for it.
Just my two cents.