Hardly anyone who surfs the internet has not seen Wikipedia. Still many people are unaware of the etymology of the name. The term wiki was actually coined by Ward Cunningham in 1995 when he wanted to create a website for common programming patterns. He chose the word "wiki" which means fast in Hawaiian, a dying language. Ward's wiki was a big success and is still used today. Six years later Jimmy Wales started Wikipedia, which was actually a side project of Nupedia, which was supposed to be a serious encyclopedia written by professors and PhDs. Nupedia never reached a 1000 articles. Wikipedia is now in the top 5 of most visited websites.
So if you want to set up your own wiki, you can.
MediaWiki
Wikipedia is running solely on open source software. MediaWiki is the specific wiki platform that grew with Wikipedia. It's great software with some quirks. Say you want to for example run a private wiki, with MediaWiki your wiki has to be entirely private. Or entire public. You can hack your way around it but there will be leaks.
Dokuwiki
I'm personally not a fan of DokuWiki but it is very common software, and it's good if you want to have your wiki partly private.
Meteorpedia
Meteor is an awesome realtime JavaScript everywhere platform. It's not so great for SEO but it's the future. Meteorpedia is a wiki built in Meteor.
More information
- Free wiki hosting discussed on this website