Personally, I have a crude and completely arbitrary classification that I've been using ever since I got into this whole operating system thing. However, whereas most people seem to classify operating systems based on what they can do, I base my classification on the people and/or organisation behind it. This classification is anything but comprehensive, but it does help me in gauging the importance of news items for OSNews.
At the very top we have the "big" operating systems - operating systems with massive developer forces, and quite often, large organisations and/or corporations backing them up. Windows, Mac OS X, Linux, and the BSDs most certainly fall into this category. For the sake of discussion, I'm lumping all the various Linux distributions together, as well as all the BSD variants.
Then there's the group of operating systems which can't be classified as "big", but aren't really hobby operating systems either. Mostly, these are systems that once had much larger followings, but have hit harder times due to parent companies folding or something similar. Here we find things like BeOS/Haiku, the AmigaOS, os/2 (eComStation) and RISC OS.
At the very bottom, we have the hobby operating systems. More often than not, they have been built from scratch, with custom kernels and userlands, and they have only very small groups of developers, working in their spare time. They do not have the financial backing of the first group, nor the lineage of the second group. You find all sorts of stuff in here, from Syllable to ReactOS, and all the other small projects out there.
I also have a "misc" category, a number of operating systems which I find, for whatever reason, very hard to classify. MorphOS and AROS are two of those; sure, they both build upon the Amiga lineage, but most of their code has been written from scratch by small groups of developers.
The reason I tend to focus on the development side when classifying operating systems - instead of what most people do, the user side - is because each person has their own sets of needs and wants that might be covered by different operating systems. I know enough people who simply can't get their work done on a Windows machine - does that make Windows a hobby operating system? I also know enough people who are perfectly happy using the AmigaOS full-time - does that put AOS on the same level as Mac OS X or Linux?
As such, I think it makes much more sense to classify based on development, because it's much more of an independently observable constant. It also eliminates a lot of those silly discussions about "my pet operating system does everything I need" vs. "it can't even do Flash!".
Which, coincidentally, takes much of the fun of OSNews away.