DokuWiki is aimed at the documentation needs of a small company. It uses plain text files and has a simple but powerful syntax which ensures the datafiles remain readable outside the wiki.
MediaWiki was custom-designed for the high-volume Wikipedia encyclopedia website; it is also used for all other projects run by the Wikimedia Foundation, which operates Wikipedia. It is also publicly available for use in other wikis, and has widespread popularity among smaller, non-Wikimedia wikis.
PmWiki is a PHP-based wiki. Features include: GPL-licensed, easy installation/customization, designed for collaborative authoring and maintenance of web sites, and support for internationalization. Does not require a database.
WakkaWiki is a now-defunct PHP/MySQL-based lightweight wiki engine, that notably spawned a large number of forks, including WackoWiki and WikkaWiki.
MindTouch is an open-source application that began as a fork of MediaWiki; it has a C# back-end and a PHP front-end.
Gitit is a Happstack-based wiki server employing git or Darcs to manage wiki history, and the Pandoc document conversion system to manage markup - among other things permitting the inclusion of LaTeX mathematical markup.
Swiki is written in Squeak. It runs on common platforms, including Mac, Windows, Linux, as well as others.
Wagn is a Ruby on Rails application that can be used as a simple wiki, a database, a content management system, or a development platform.
XWiki is a Java-based wiki engine with a complete wiki feature set (version control, attachments, etc.) and a database engine and programming language which allows database driven applications to be created using the wiki interface.
WikidPad is a free, open source personal use (single-machine) wiki with native support of international characters (Unicode).
ConnectedText is a commercial Windows-based personal wiki system with features including full text searches, visual link tree, customizable interface, image and file control, CSS-based page display, exports to HTML and HTML Help, and plug-ins.
Zim is a free, open-source standalone wiki based on Python and GTK with a WYSIWYG editor.
Jive (formerly known as Clearspace, Jive SBS and Jive Engage) is a commercial J2EE application, made by Jive Software, which combines wiki, blog and document management functionality. Jive uses WYSIWYG editing, and includes workflow management.
Confluence is a commercial J2EE application which combines wiki and some blog functionality. Its features include PDF page export and page refactoring, and it can be run on any application server using any RDBMS backend.
SamePage is a commercial J2EE application that combines wiki and blog functionalities in an enterprise collaboration solution. It is a SaaS application or software download that utilizes WYSIWYG editing.
Traction TeamPage is a commercial enterprise wiki, blog, document management, discussion and tagging application based on the principles of Douglas Engelbart's On-Line System (NLS) which aggregates multiple blog/wiki spaces using a sophisticated permission and inline comment model.