What Python 3 versions I can use (November 2018 edition)
Back several years ago, I did a couple of surveys of what Python versions I could use for both Python 2 and Python 3, based on what was available on the platforms that we (and I) use. What Python 2 versions are available is almost irrelevant to me now; everything I still care about has a sufficiently recent version of 2.7, and anyway I'm moving to Python 3 for new code both personally and for work. So the much more interesting question is what versions of Python 3 are out there, or at least what major versions. Having gone through this exercise, my overall impression is that the Python 3 version landscape has stabilized for the uses that we currently make of Python 3.
At this point, a quick look at the release dates of various Python 3 versions is relevant. Python 3.4 was released March 16, 2014; 3.5 was released September 13, 2015; 3.6 was released December 23, 2016; 3.7 was only released this June 27, 2018. At this point, anyone using 3.7 on Unix is either using a relatively leading edge Unix distribution or built it themselves (I think it just got into Fedora 29 as the default 'Python 3', for example). However, I suspect that 3.6 is the usual baseline people developing Python 3 packages assume and target, perhaps with some people still supporting 3.5.
At work, we mostly have a mixture of Ubuntu LTS versions. The oldest one is Ubuntu 14.04; it's almost gone but we still have two last 14.04 servers for a couple more months and I actually did write some new Python 3 code for them recently. The current 14.04 Python 3 is 3.4.3, which is close enough to modern Python 3 that I didn't run into any problems in my simple code, but I wouldn't want to write anything significant or tricky that had to run in Python 3 on those machines.
(When I started writing the code, I actually asked myself if I wanted to fall back to Python 2 because of how old these machines were. I decided to see if Python 3 would still work well enough, and it did.)
We have a bunch of Ubuntu 16.04 machines that will be staying like that until 2020 or so, when 16.04 starts falling out of support. Ubuntu 16.04 currently has 3.5.2, and the big feature it doesn't have that I'm likely to run into is probably literal string interpolation; I can avoid it in my own code, but not necessarily in any third party modules I want to use. Until recently, the 16.04 Python 3.5 was the Python 3 that I developed to and most actively used, so it's certainly a completely usable base for our Python 3 code.
Ubuntu 18.04 has Python 3.6.6, having been released a few months before 3.7. I honestly don't see very much in the 3.7 release notes that I expect to actively miss, although a good part of this is because we don't have any substantial Python programs (Python 3 or otherwise). If we used asyncio, for instance, I think we'd care a lot more about not having 3.7.
We have one CentOS 6 machine, but it's turning into a CentOS 7 machine some time in the next year and we're not likely to run much new Python code on it. However, just as back in 2014, CentOS 7 continues to have no version of Python 3 in the core package set. Fortunately we don't need to run any of our new Python 3 programs on our CentOS machines. EPEL has Python 3.4.9 and Python 3.6.6 if we turn out to need a version of Python 3 (CentOS maintains a wiki page on additional repositories).
My own workstation runs Fedora, which is generally current or almost current (depending on when Fedora releases happen and when Python releases happen). I'm currently still on Fedora 28 as I'm waiting for Fedora 29 to get some more bugs fixed. I have Python 3.6.6 by default and I could get Python 3.7 if I wanted it, and my default Python 3 will become 3.7 when I move to Fedora 29.
The machine currently hosting Wandering Thoughts is running FreeBSD 10.4 at the moment, which seems to have Python 3.6.2 available through the Ports system. However, moving DWiki (the Python software behind the blog) to Python 3 isn't something that I plan to do soon (although the time is closer than it was back in 2015). My most likely course of action with DWiki is to see what the landscape looks like for Python 2 starting in 2020, when it's formally no longer supported (and also what the landscape looks like for Python 3, for example if there are prospects of significant changes or if things appear to have quieted down).
(Perhaps I should start planning seriously for a Python 3 version of DWiki, though. 2020 is not that far away now and I don't necessarily move very fast with personal projects these days, although as usual I expect Python 2 to be viable and perfectly good for well beyond then. I probably won't want to write code in Python 2 any more by then, but then I'm not exactly modifying DWiki much right now.)