Can you have a photography career without a degree or do you have to have a degree?

I would guess that most photographers do not have any formal training in photography these days (whether by school or apprenticeship)...camera and lens technology is cheaper than ever and post-processing skill is almost irrelevant as the tools themselves get smarter and pre-packed action-sets or filters are used.

What this means is, there are an absolute ton of hobbyists that have flooded the profession with good images and they'll take little money for them. See the death of photojournalism and nature photography for good examples.

What this leaves you with, if you want a career in photography, is playing to people's need for photographs of themselves. Weddings and portraits are the best types of photography to run your business on. For these types, a portfolio means more to your future clients than your degree.

That being said - the ability to control light is what makes a good photographer great. There are an absolute plethora of shooters out there that don't know the first thing about flash, studio lighting, or mixed lighting. Almost ironically, these are exactly the things you'll learn during a photography program.

So, while it is absolutely possible to shoot professionally without a degree - I would say it's highly advisable to make sure that you self-teach all of the topics that you would find in a class syllabus.

As an aside: I began working in a studio in high school and started college as a photo student. I quickly switched to business marketing, having realized that I was getting more tutelage at the studio than I would get in school. Having run a photo biz - I can absolutely advise going down this path. There's a whole lot about running a business...finding leads, writing contracts, accounting, etc...a whole lot more to it than you'll know no matter how much you prep.