Free Wiki hosts
Wikipedia article (Very good list of wikis)
atwikiPopular wiki, looks ok but I have not used it.
MediawikiMediaWiki is a free software wiki package originally written for Wikipedia. It is now used by several other projects of the non-profit Wikimedia Foundation and by many other wikis. Needs to be downloaded so not as easy as the web based wikis.
pbwikiMust be the easiest wiki to set up. Great to use. Clean pages.
pmwikiBasic look but good FAQ. Default upload limit 50k but it can be changed to 1MB.
Seed WikiThis has both a free (some ads) and paid version. Often quite hard to navigate around the site and not really user friendly.
WetpaintHas side bar with ads, and right side bar with menu so it takes a lot of screen space. Tedious setup compared to most but gives good choice of templates etc. Seems to work well (used for this wiki).
WikicitiesThis wiki is not really for the beginner. Often hard to navigate. Does have some nice features though.
WikispacesVery good wiki. Generous upload. Looks a bit ordinary is only downside.
XwikiVery complex and hard to understand for the beginner. Need to have a decent wiki background. Registration required.
ZohoFull function wiki. Good WYSIWYG editing and pages can be locked.