A wiki is a web page or set of web pages that can be edited by the users rapidly and collaboratively. Wikipedia is probably the most famous of all wikis and their underlying engine is called MediaWiki. It’s open source and available for install on mtheory.
Wiki’s allow easy edits to webpages and enable many people to collaborate, however they are a prime target for spammers and unless you expect a largish number of people to contribute we would suggest you avoid a wiki. Either that or you need to lock it down quite a bit to eliminate the spamming problem. This somewhat negates some of the benefits of a wiki. The support pages on the old mtheory site were based around media wiki and suffered from large numbers of unwanted edits never mind the creation of hundreds of unwanted pages by spammers. In saying that, if you are willing to monitor and have multiple contributors you can make it work.
In general most web based things can be installed and made to run under mtheory. SQL databases can be readily generated and custom frameworks and platforms can be installed if required and you have a genuine need. If you’re looking to do something unusual just ask.