Wikis are simple, light-weight concept. Unless you plan to document all of human knowledge, use simple, light-weight wiki software.
PM Wiki
Yay!
Open source, PHP + flat-file wiki.
Insanely easy to install (drop onto a server that runs PHP, make sure permissions are set to execute, that's it). Painless to customize. Well maintained. Stores data as individual text files, with some metadata code.
PHP Wiki
Sure.
Another open source, PHP + flat-file wiki. Usually comes with cPanel+Fantastico for push-button install.
TikiWiki is also a common Fantastico install, so it's easy to try out. But it's not really a wiki. It's more of a Russian space station glued on to an office suite.
DokuWiki
Okay.
Another open source, PHP + flat-file wiki.
The only (?!?) wiki that stores data in pure plain text files with no additional code, metadata or formatting. Text files can be mass-moved in and out of storage without any modification. To create a wiki sub-directory, you just create a sub-directory and put files in it. Why is this the only wiki that does this? Why doesn't everything do this??
It can be a finicky to install. The default template is fairly nice (for a wiki), but if you don't like it, it can be a pain to customize.
MediaWiki
Avoid.
Runs wikipedia, so many people consider it the wiki of choice. If you have less than a 100,000 pages, it probably should not be the wiki of choice.
Installation can be complex. Customization can be a nightmare. Skinning isn't easy. It requires a database (MySQL?) for storage. It has a tendency to blow up and take the database with it (not really risk with flat files).
Also in this category: Twiki. "Enterprise wiki" means you need to hire an IT support person to run it.