DokuWiki is an amazing, simple and customizable Wiki system
DokuWiki is one of those "I can't believe we've never covered it!" tools. It's not new; it's not cutting-edge. It's solid, and tested, and it's been around for years, and it is one of the best Wiki systems on the planet, in my opinion.
DokuWiki is great for content sites where you have one editor and the rest of the world just reads the wiki; it's also great for collaborative wikis, and there was a time when my own personal site ran DokuWiki, too.
I've been working with DokuWiki for years now, and have deployed and managed it several times. Just so you could see how customizable the layout can be – here is the official DokuWiki page, and here is an installation I customized.
In a nutshell, you can customize everything. There are templates you can download and very easily install, but you can also make your own very easily. There is a great plugin system, too: to install a plugin, you just feed its URL into a box, and click Install. That's it; your DokuWiki installation would download it, unzip it and install it.
There are plugins for everything, from new syntax, to making your wiki into a blog, to managing access rights in a different way, to changing navigation ... in short, just about anything really. And as a wiki system, it is far simpler than MediaWiki (the stuff Wikipedia runs on).
Bottom line: Highly recommended; simple, elegant, free, and has an active community. What's not to like?