The great news is hat wiki's are becoming mainstream these days and increasingly we are being approached by people particularly in government who want to adopt some type of collaborative and spontaneous editing environment that made wiki's famous. Unfortunately some of the elements of wiki's that have made them successful also makes them more difficult to adopt by non-technical and more bureaucratic organizations.  

Resources like Wikipedia have proven how valuable information can be freely organized by a community of users quickly and efficiently. Wikipedia is a great model and fortunately they are built on open source software so it is a model which is replicable. The user model of Wikipedia is not something however that most organizations would feel comfortable with. Most organizations would want to know who made what change and ensure that no anonymous modifications of the wiki were possible. Others are just worried about the public nature of well known wiki's.

Many definitions of wiki say that it is software that allows users to edit any page of the site. This was indeed a default with which many wiki applications still have, however wiki spam has made this option less viable and certainly much more risky for all but for those communities that are super active and attentive. Most organizations do have structures that require information and access to be restrict pages to a group, role or individual. Private spaces for teams to develop ideas without scrutiny of the whole organization is positive, but each team should not need to maintain it's own wiki.

Wiki markup is the simple text markup that allows people to quickly apply simple formatting to text by wrapping simple character combinations like '!!', '*' or '==' around a word. Unfortunately, although very simple, many people have opted to create variations which have become very popular with some wiki's. Unfortunately it is usually difficult for users to adapt to learning these codes unless they use them a lot and switching between formatting can be brutal for the user. I'd argue that the markup is probably the largest single element uniting things described as a wiki. Some also include simple WYSIWYG editors but even there they generally produce wiki code so that it is possible to easily compare versions of a document with a human readable comparison. In Drupal we've described one way to do this using a modified quicktags module.

It is worth noting that there are quite a few definitions of wiki that don't mention formatting at all.

For me a wiki wouldn't be a wiki without versioning. How else would you allow for multiple contributions from a community with diverse points of view? However, versioning alone does not make a wiki as in Drupal any type of content can have changes tracked in this way.

Wiki's should also have a way to create links to existing wiki pages and links to new pages. All wiki software provides this functionality and it would be pretty silly to have a wiki that just allowed editing one very, very long page. There are a few ways to do this in Drupal so that it is more intuitive than linking to other pages. Also, the wiki tradition of creating links to empty pages is a great way to inspire people to add new content.

There isn't consensus on what folks mean when they say that they want a wiki, since there is such a wide variety of tools and use cases. By talking with our clients we can get a sense of what their needs are and build a custom environment that allows them to have a collaborative environment that meets their needs. Drupal is a great platform for this approach to delivering wiki's because it is so very flexible. Internally we have a fairly standard wiki that allows us to keep track of basic client notes, but we can then easily convert that wiki to a different content type that extends the wiki to include project management tools when we need that. Others might require a collaborative editing environment to organize events or time-lines, and we could easily build a content type that incorporates that in Drupal without doing any coding.