First of all, click here to visit TiddlyWiki homepage and play around a little bit. Then return here.
OK, did you get all that? Great stuff, isn't it?
I needed some sort of small Wiki (for my personal project), which could be run on my local computer, preferably even without Apache (i.e. with its own embedded server). TiddlyWiki is exactly that and more - it does not need any server. In fact, it does not need any server-side logic at all!
Can this even be called "Wiki"? How do you save changes? Basically, you just use "Save as" option in your browser (although that poses some problems and you should use the built-in save mechanism). You can easily carry whatever Wiki you want with you as a single file on USB stick or you can create and edit it at home and then upload it on your server (with editing controls disabled, so that you don't confuse the visitors).
UPDATE: If you want something more traditional, server-based, but without need of standalone server or database, try Instiki, written entirely in Ruby.