There are quite a few open source packages for wikis out there. Quite a popular choice is MediaWiki, the same software that runs Wikipedia and its sister sites, along with many other popular wikis out there.
However, today I'm going to focus on something a bit... well, lighter.
DokuWiki is a GPL 2-licensed, PHP-based wiki system. As the name suggests, it is slightly focused towards documentation, although of course can be used for any purpose.
Unlike many wikis, DokuWiki uses no database and instead works with flat files. This approach has advantages and disadvantages compared to using a database to store information. On the positive side, it means you don't have to have any specific hosting requirements, and DokuWiki will run anywhere that PHP will (often ven on low-end shared hosting packages). The downside is that it can be slightly sluggish at times, although it makes good use of a caching system to avoid most slowdowns for when you're not logged in.
Despite this, it has an array of features, including (of course) full version history and revision support, diff-style change comparisons, namespaces, powerful access control lists and more.
Personally, I find Dokuwiki very useful - especially for applications where you don't want or need the complexity of a system like MediaWiki. I use it for a documentation wiki for my small open source scripts on my site, and it works for that purpose well. Admittedly, I haven't tried it out in a situation with lots of users and changes, but if you've got a small site which could use a wiki-based site, I would recommend DokuWiki.
DokuWiki is free under the GPL, runs anywhere PHP does and can be downloaded from the official site.