Wiki written in python as used by Ubuntu, FreeBSD, Debian and others. Uses flat file storage by default. Lovely.
Local HTML only wiki, all in one file. Useful for personal notes and so on. Not sure how it saves.
JiglueHood allows you to create a free "group space" including a wiki, mailing list and possibly more. It uses the jiglu auto-tagging engine to link stuff together.
Moulin allows you to download different languages versions of Wikipedia on a single CD. It's aimed at developing countries where internet access is less common.
Wikia allows you to create free (I think) MediaWiki installs. They currently host over 4'700 apparently.
Wikka is a very simple PHP/ MySQL wiki. It has very basic functionality, without the advanced features of something like MediaWiki, but it's extremely easy to use.
Create web sites just by entering some text at jottit.com. A handy little app, with a beautifully simple interface!