Stand Alone Wikis
Corendal Wiki - A free and open source wiki package directed at corporate users. It’s been a while since it has had any updates.
DokuWiki - Aimed at small companies’ documentation needs. Offers templating and plugin support.
FlexWiki - A free and open source wiki built on the .NET framework.
GetWiki - A modified version of MediaWiki that provides new features including XML importing.
IpbWiki - A system that integrates MediaWiki with Invision Power Boards to make for a whole new wiki experience.
JAMWiki - A Java based clone of MediaWiki that uses the same syntax for things such as footnotes, templates and more.
MediaWiki - The same software that powered the omnipresent Wikipedia, MediaWiki is a PHP based, customizable system that is one of the most popular solutions due to its familiarity.
Mindtouch - Free and open source wiki if you choose to run it on your own host, but if you prefer a managed solution for an enterprise install, they offer various managed solutions.
MoinMoin - Has different built-in templates and allows for the support of documents. Popular framework being used by the likes of the GNOME and Ubuntu sites.
PHPWiki - One of the oldest wiki solutions, first appearing in December 1999.
PikiePikie - Files are stored in such a way that they are easily manipulated with a text editor on the server, and has safeguards against spammer attacks that make it easy to roll back edits.
PmWiki - Built more for non-IT people and those that have no wiki background. Easy to change skins and appearance.
QwikiWiki - Built for speed and minimal features, QwikiWiki is built for ease and a quicker learning curve.
TikiWiki - A content management system capable of handling many different jobs, but as the name implies, it favors wikis.
Wikka Wiki - Forked from Wakka Wiki, Wikka has some new features such as support for mindmapping.
@wiki - A completely free wiki service that offers WYSIWIG editing and password protected posts.
ClearWiki.com - Gives you your own subdomain, up to 10 users, 256 MB of storage for the free accounts, does have paid solutions with more of everything. Directed towards businesses.
EditThis.info - Allows you a free 25 MB MediaWiki install with unlimited users and pages.
eTouch SamePage - Allows teams to work in a collaborative environment on projects, free version allows for up to 5 users, 3 projects and 15 pages.
LittleWiki - Create a public or private free wiki with WYSIWIG or plain text editors.
Netcipia - Free wikis with no limits on what you can do and even allows you to monetize your site to sell your expertize on a subject.
On-Wiki - Somewhat directed towards academics and business in that it allows media, graphs, plotting and more for free.
PBWiki - Offers free wikis, but they only have 10 MB of space. Paid solutions start at $99.50 a year. The service offers password protected wikis for private or corporate situations.
ScribbleWiki - A MediaWiki hosting service that has free accounts for personal use and paid solutions for companies that need their pages ad-free. Site has tech support and a few other premium features.
ViaWiki - Offers free 25 MB sites and paid solutions for multiple users up to an unlimited number.
Wetpaint - A free wiki farm that focuses on bringing together the wiki format with blogs and forums. Very much directed towards fan-style sites.
Wiki-Site - Free MediaWiki accounts for individuals and groups, paid accounts get unique domains, access to stats and no advertisements, amongst other perks.
Wikia - Co-founded by Jimmy Wales of Wikipedia fame, Wikia has to approve each wiki that is started, and they have to be believed to draw a large amount of traffic and editors.
Wikidot - 300 MB free Wiki for whatever you want, Google AdSense can be placed in your wiki with you keeping 80% of the revenue.
Wikispaces - Starts at free 2 GB site for friends and families up to paid white label solutions.
XWiki -Offers free solutions as well as paid options for enterprise users. Allows for application development and embedding in pages, along with RSS feeds to keep teams up on changes.