http://wiki.python.org/moin/Python2orPython3 was created recently to answer just such a question, quite recently in fact (some people were asking similar questions and the issue of the quality of the stock answers was raised in comp.lang.python).
If you're doing something completely new that will never interact with older code bases, Python 3 seems like the best choice. This is where the language is ultimately going.
However, if you have to integrate with almost anything in 2.x land, such as 3rd party libraries, you may have no choice but to keep using 2.x for awhile. As usual, even from this older version, there are ways to voluntarily import future capabilities so that your code is as 3.x-like as possible.
Both are stable. Both will continue to be stable for a long time.
The main difference lies with third party library support. There are a number of third party libraries that don't work with Python 3 yet. They will get ported eventually. If you want to use a library that doesn't support 3, then the choice is made for you.
The second difference lies with Linux distributions. On most distros you can just install the "python3" package and everything works, on a few distros you'll have to install Python 3 yourself or hunt down the right package repository (my info may be a year behind or so, I'm not sure). This also applies to third party libraries -- even if the library supports Python 3, your distro might not have a package for it, even if it has a package for that library for Python 2.
It's fairly easy (most of the time) to write code for Python 2.x that converts to Python 3 code with the bundled "2to3" converter. I do this for any script I might ever want to give to someone else or run on a computer that's not mine. Otherwise, I just write straight Python 3 code. Assuming, of course, that I don't need some library.
This is what worries me about Python: Python3 has been stable for a long while now, yet major projects (SciPy, Django) remain on 2.x, with no clear deadline for being ported to Python 3.
Contrast this to Ruby, where Rails 3 is 1.8-compatible but recommends 1.9. Ruby 1.9 is being used in production even though it's not completely stable yet. In short, Ruby is clearly evolving, major libraries are constantly being updated for the latest version of the language, and everyone in the Ruby community has a strong sense of "getting better all the time."
Python 3 is a better language than Python 2. That it's taken so long to become the canonical version makes me wonder about Python's future.
Python 3.x is different in a bunch of little ways from 2.x. Just like you say Rails 3 runs on Ruby 1.8 and 1.9, most Python libraries will run on 2.5, 2.6, or 2.7 (often 2.4 as well) without modification. Python 3.x breaks these libraries. Python 2.7 is also several months newer than Python 3.1.
It reminds me of the 2.4 -> 2.6 transition for the Linux kernel. People were using 2.4 for a long time. Heck, you can still find Linux 2.4 in the wild.
>Ruby 1.9 is being used in production even though it's not completely stable yet
That's the difference. Without being insulting, Ruby is used for web sites that don't matter - if your twitter feed about twilight goes down nobody cares.
Python also gets used for stuff where a lot of $$$ dissapear if it goes too wrong
I think that once the Django team announces their intention to port most of the auxiliary applications will take notice and follow suit. I base this on how the (better) auxiliaries have been pretty good at keeping in sync with Django's releases.
If you have to ask, I would highly recommend 2.x ! Nobody of note is using 3.x in production. It's nice, but not backwards compatible with the huge pool of existing code / docs; which is one of python's strongest suits, especially if you're coming to the language fresh.
Google App Engine SDK uses Python 2.5, I had 2.6 installed and had to revert. 3 drops some features, adds some others. You can import 3.x features in 2.x from __future__, see: http://docs.python.org/library/__future__.html
One of the less useful features dropped is 'somestring'.encode('rot13') :P
Speculatively, there are more than 2 Pythons. Python, like perl has become a family of languages. Some time ago Perl Mongers accepted that Perl 6 was not the next version of Perl but a new language in the Perl family. I suspect Python 3 is to Python 2 as Perl 6 is to Perl 5. Google's Go is also a language in the python family I think.
There are many more than 2 pythons. Several versions 2.6, 2.4, 2.2 happily in use in the wild. Not to mention jython, Stackless, IronPython and the like.
Python 3 is not backwards compatible with Python 2. The developers have always stated that Python 3 will be a 5 year project until the entire standard library is ported.
less cynically ... perhaps the poster wanted the personal opinions of HN hackers, many of whom probably have first-hand experience with Python and might be able to give more personalized answers than what's on FAQ pages
so if that's the case, here's what I should do. i'll begin preparing a series of questions to post to HN in the coming weeks, to keep in the same spirit. Rough list to start with:
1. where do babies come from?
2. what is PageRank?
3. what sorts of languages can you write iPhone apps in such that they are allowed in the Apple store?
4. why might I want to write an app in C versus in BASIC?
Actually, if you went one step beyond and asked for opinions or non-obvious answers to any of those, I'd consider that perfectly suitable for the site.
For example
2. is there an open source implementation of PageRank?
3. any tips on how to fake handwritten Objective C so Apple will accept my app?
4. I wrote my app in BASIC instead of Objective C and Steve Jobs said it was okay
here's one more to add to your list: if you do an automated text meta-analysis of "Ask HN" titles and see what words/phrases are correlated with more upvotes, then post your analysis on a blog post, i'm sure people would upvote you like crazy ;)