Instiki, the Ruby-based Wiki, seems popular for one feature in particular: it is its own web server. Installing Instiki requires no set-up or configuration of web server (or database) software, you just run it and it goes. This makes it especially useful for running on your own desktop: download and run, and you have a private browser-based wiki for your personal notes.
This feature of Instiki is also its biggest detriment. Instiki must open its own port to behave as a web server, and on anything but your own computer (such as web hosting), you do not have permission to open a new port. Even if I had administrator privileges on a server, I would think twice about dedicating a port to a wiki. Perhaps this is less of a barrier for corporate intranets, a sweet spot for wiki use. For my purposes, I need a personal wiki, but I need it publicly available.
Still my wiki of choice, Kwiki, the almost-as-easy-to-install Perl-based wiki, is up to verison 0.36 (2004-12-18). After installing the Perl modules from CPAN, it's similarly one command to install a new wiki in an existing Apache document directory. The plugin platform is maturing steadily, though it's still pre-1.0, as are a bunch of the newer plugins.
If you have an Apache server running on port 80 on the same box, you can configure the server to proxy requests to another server or another port on the same server. The ProxyPass directive can be used to set this up on a virtual server basis or on a directory basis.
http://httpd.apache.org/docs/mod/mod_proxy.html#proxypass