Wikipedia mainly runs on MediaWiki, the wiki platform written in PHP, and there are a number of customized modifications of the wiki, built for other Wikimedia Foundation projects, or for external projects. (See Wikipedia:MediaWiki)
There have also been scripts written specifically for working with Wikipedia as well as with other MediaWiki-based sites, such as "wiki format" scripts for text editors, bots, extensions for browsers, and site tools that help with particular aspects of editing Wikipedia.