A few years back - in 2005 - I did a research project to find a wiki for our internal use at work. We downloaded it, installed it, and it got very - very - light use...just a handful of pages were created.
Then about 18 months ago, we came up with a specific need, and from that requirement launched a very brief search, installed a wiki, and it has been well used since that time. In fact, since the initial use, we have conceived of other ways to use the wiki and it continues to be a more valuable tool all the time.
Not sure how a wiki can help? A great site to inspire wiki use is Grow Your Wiki, and particularly the 7 effective wiki uses and the companies that benefit from them will infuse any brainstorming session or grass roots movement with ideas.
Back to my search, it would have been handy - in both instances - to have had access to Cameron Chapman's recent post 100+ More Wiki Tools and Resources over at Mashable. It does not violate my aversion to lists, as it is simply a compilation with very brief descriptions (one sentence) of the wiki or wiki tool, and a link to a page where you can get more information. Very concise, but a great place to start a search (Cameron Chapman however could possible create a new list aversion). But the Wiki list is great - I hope it is kept up to date, or an updated posting is made at regular intervals.
To really 'talk the talk', WikiIndex is a wiki site about everything wiki, including lists of wikis and resources. It's too much to start a search there, but looks to be a great resource - and it's a wiki.
Any time is a good time to start a wiki, but from our experience, have an initial need or demand that will attract use. Have some wiki resources available. Then wIth participation will come some innovative ideas on other uses. This can help too.