If I was going to start an open source project using Python what version should I use to ensure that the vast majority of users can use it on their system?
I'm the kind of person who quickly jumps to the next version (which I'll do when Python 3 comes out) but many people may be more conservative if their current version seems to be working fine. What version would hit the sweet spot but still allow me to enjoy the newest and coolest language enhancements?
You can use different versions of python on each machine. 
Coding something new, I would not use anything less than python2.5. You can do apt-get install python2.5 on stock debian stable. 
For windows, don't really worry about it. It's very easy to install the python2.5 msi. 
If the users can't be bothered to do that, you can deploy an executable with py2exe (so simple) and build an installer with inno setup (again simple) then it will behave like a standard windows application and will use its own python dlls, so no need to have python installed. 
Like Peter said: keep in mind the transition to 3.0 but don't build on it yet.
Which Version of Python to Use for Maximum Compatibility