MacPython: This is python.org's installer of the latest Python framework build, along with some Mac-specific apps to help use it, like IDLE.app. This is the default recommendation of the MacPython community. See the Python download page for the Mac for instructions on how to download the installer and run it.
ActivePython: An up-to-date, commercial and free (as in beer) distribution of Python. ActivePython installers for a large number of platforms (including Mac OS X 10.3, 10.4 and greater, PowerPC and Intel) are available. Note that ActivePython does not include readline support, but it can be added.
Apple: Mac OS X comes with a pre-installation of Python, usually one or two years old. This can be sufficient for some needs, but the MacPython community recommends installing a newer, more capable, version. Don't get rid of the Apple version, though! It's used by some system utilities.
Fink.: a project that packages up many open-source projects in a Debian-like system of installers with explicit dependencies. A version of Python can be installed with Fink, but it's not recommended by some people in the MacPython community, mainly because too many prerequisite packages have to be installed for Python, and some of them seem to conflict with system packages.
MacPorts: Another project bundling open-source software for Mac OS X and Darwin is called MacPorts. Again, Python can be installed with this software, but it isn't recommended by some people in the MacPython community, mainly because it's complicated and involves installing prerequisite packages. On the other hand, MacPorts probably has the by far largest amount of ready-to-run python modules available, all installable via a simple command. The project was previously known as DarwinPorts.
Homebrew.: yet another project that packages Python and many other projects for Mac OS X.