Ranked in these QuestionsQuestion Ranking
Pro The de facto standard
Mediawiki is a widely used wiki engine. It is used to power Wikipedia and thus most people will be more comfortable/accustomed to using MediaWiki.
Pro Version control
MediaWiki allows viewing past revisions of pages.
Pro Free and open source
Licensed under GPL.
Pro Thanks to Wikipedia it is thoroughly documented
Pro It has a powerful templating system
Pro It has a usable WYSIWYG editor
Pro Great multilingual support
MediaWiki has full support for over 65 languages and partial support for over 300.
Pro Runs on any PHP server
It requires a webserver running PHP 5.2 or later of any kind.
Pro Multiple database support
MediaWiki can store data in MySQL, PostgreSQL, Oracle and SQLite databases.