A professional physics career without a degree? I learned programming as a child, for fun. Now I am working as a programmer, even though I got a business major degree.
I wonder if there are career paths for doing physics other than becoming a researcher in a University or a professor, that are not all about credentials?
 A: Although I haven't researched it, you can learn some physics and try to get into computational physics. There is some industry for it out there (e.g the materials sector, though I would doubt they hire anything but Phds). However, if you're a really great programmer and bring in your ideas and experience creating software, with the additional knowledge of being able to conduct simulations of physical systems and conduct solid quantitative analysis, then why not. There is also a market for physics specific software. For example, you can learn electrodynamics and create a (hopefully open source or atleast free ;)) counterpart to Simion. If developing independent software alternative is too much, you can contribute by creating physics modules, writing patches etc. to products like Sage. There are more possible places where you can develop, off the top of my mind the ROOT develeopment team at CERN has two non-physicists working for them. 
The best strategy I would recommend is to start learning basic physics, and simultaneously research what is going on at the interface of physics and computation. One guide would be to look at the conferences and seminars that are held on the subject and find out what currently engages physicists. For example, have a look at: Physics and Computation 2010 and Conference of Computational Physics. Look at the titles of talks and submitted papers, the workshops, tutorials etc. Find more on the web (keyword search on the arxiv) etc, and you will get a rough idea of the status of the field. Start working on something, make some contributions to open source initiatives or get your own results, basically get some credentials so that employers might pay attention to you and you might find yourself working along with Phds.
A: Are you asking about never getting a formal education and never getting an academic job but still doing physics? For example you have a rich aunt, you don't have to work so you can write papers from the library in your mansion, where you learnt physics? I would say that would be hard because you need the communication with other physicists. So if you go regularly to the near by university to attend seminars and discuss and collaborate then why not.
A: No, you haven't got a chance unless you want to be a gofor in an R&D department of an engineering company. Physicists become programmers because physics jobs are hard to come by and difficult to do compared to programming, not the other way round.
Edit:
Thinking about it further, yes, you can forge a professional physics career without a degree, as long as you target a company where the applicants don't have a degree. I.e, do voluntary work where you don't expect to get paid much, or where the work conditions are poor, so that no professional physicist would want to work for that company.
