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(Note: None of these applications require a database, or any extras beyond a recent version of Python installed on your server.)

First we have Vellum, a Python blogging application with a Plugin extensibility model for RSS feeds and such. Vellum provides page cacheing (but only after the first time a page is requested) and has some of the typical goodies (like templates) as well.

Pyblosxom is an implementation of Blosxum (a Perl application), but in Python. Both Pyblosxom and Blosxum are very simple, but fairly powerful, weblogging tools.

And, of course, there is Spyblog -- Blogging about as simple as it comes. (One Python file and a template. Done.)