One of the most useful attributes of introducing a wiki into an organization is its viral nature. Once a few people begin to use the wiki, they often realize that they could be even more efficient if only their colleagues were using the wiki too.
More people using it means they can each encourage their direct contacts and collaborators to join, thus laying the groundwork for exponential growth. This Viral growth increases the value of the wiki to each user, because the number of people with which one can collaborate increases. Soon, wiki accounts are spreading exponentially.
Search for simple results that work - that's the best way to get the expansion. When you have several easy examples, they can be used to spread the usage to larger groups or projects. This will be easy food for champions to spread. Highlight good examples of usage or content by linking them from the wiki main page.
When you have regular newsletters to the whole organization, this will also be a great place to mention the examples.
Dwight is compiling his quarterly marketing report with his teammate, Jim. He and Jim use the wiki to add their respective statistics and compile the department's report. However, when the report is complete, it must be submitted to their manager, Michael, who will have comments. Rather than emailing the report to Michael and then manually incorporating Michael's changes, Jim realizes it will be far easier for him if he has Michael do it directly to the wiki document. Michael, in turn, has to submit the report to the regional director, Jan, who will have her own changes. So Jim signs Michael up for the wiki, and then Michael gets Jan to use the wiki. It can expand even more widely from there.